DVBE's Numbers English Contest

Solution to Contest #13

2011-12-10T12:27:00.005-07:00

This numbers English contest has lots of numbers English to translate into calculation. It also requires some logic to set up the calculation.

The question seems quite tricky:

What is the expected loss in profit from March to April?

Some of you may be asking: "How can we have a loss in profits?" After all, losses and profits are opposites of each other; we should only have one or the other, right?

To explain this, let's consider a company that has a profit of $2,000 in Month 1 and a profit of $1,500 in Month 2. There is a $500 loss in profits from Month 1 to Month 2. Now do you understand how words are used in this way?

We need to start with the end of March production figures to build our figures for March and April.

At the end of March, an oil well was producing 50.5 m3 of oil per day and 72.1 m3 of water per day. Each month, the well's oil production decreases by 1.855% and water production increases by 2.011%.

To get the figures for the end of April, we simply make these calculations:

Oil rate = 50.5 m3 x (1 - 0.01855) = 49.56 m3 per day.

Water rate = 72.1 m3 x (1 + 0.02011) = 73.55 m3 per day.

Average oil rate = (50.5 + 49.56) /2 = 50.03 m3 per day

Average water rate = (72.1 + 73.55) / 2 = 72.82 m3 per day

Total oil production = 50.03 m3 / day x 30 days = 1,500.9 m3
Total water production = 72.82 m3 / day x 30 days = 2,184.6 m3

The figures for March are going to be more difficult to calculate because the 50.5 and 72.1 are at the end of the month. In English, it is important to base the % calculation on the starting figures, which, in this case, are for the beginning of March, which is what we are trying to solve. So the calculations work like this:

Oil rate = 50.5 / (1 - 0.01855) = 51.45 m3 per day.
Water Rate = 72.1 / (1 + 0.0211) = 70.61 m3 per day.

Average oil rate = (51.45 + 50.5) / 2 = 50.98 m3 per day.
Average water rate = (70.61 + 72.1) / 2 = 71.36 m3 per day.

Monthly oil production = 50.98 x 31 days = 1580.4 m3.
Monthly water production = 71.36 x 31 days = 2,212.2 m3.

The next step is calculating the profits for March and April:

It costs $140,250 to operate this well each month.
[It also costs] $51.90 to process one cubic meter of oil and $15.50 to dispose one m3 of water.

For March the costs are: 140,250 + 51.90 x 1580.4 + 15.50 x 2212.2 = $256,563.
For April the costs are: 140,250 + 51.90 x 1500.9 + 15.50 x 2184.6 = $252,008.

Oil price is expected to be $575.00 per m3.

Supposedly, the petroleum company already knew the price of oil in March, but this figure was not provided. The "expected" price is for April. Because this information is somewhat vague, we can only use the best information we have. We will assume that the oil price for both months is $575.00 per m3.

March revenues = 1580.4 x 575.00 = $908,730
April revenues = 1500.9 x 575.00 = $863,018.

What is the expected loss in profit from March to April?

March profit = $908,730 - $256,563 = $652,157
April profit = $863,018 - $252,008 = $611,010

So the loss in profits (from March to April) is $652,157 - $611,010 = $41.147

If you were watching your calculations closely, much of this loss in profits can be attributed to March having one extra day.

Contest #13

2011-11-08T19:19:00.003-07:00

At the end of March, an oil well was producing 50.5 m3 of oil per day and 72.1 m3 of water per day. Each month, the well's oil production decreases by 1.855% and water production increases by 2.011%. It costs $140,250 to operate this well each month, which including operator salary and amortization of equipment. Additional costs are $51.90 to process one cubic meter of oil and $15.50 to dispose one m3 of water. Oil price is expected to be $575.00 per m3. What is the expected loss in profit from March to April?

Solution to Contest #12

2011-11-08T18:55:00.002-07:00

Bigby Co. & Figetz Inc. are manufacturing competitors. They each sell their widgets for $45.00 a piece. Bigby's fixed costs are $101,900 a month. Figetz's fixed costs are 21.1% lower than Bigby's. Per widget, Figetz has a variable cost of 25.75% of the sale price. The cost is 3.5 percentage points more than Bigby's variable costs.

Bigby's fixed costs = $101,900 per month.
Figetz's fixed costs = $101,900 x (1 - 0.211) = $80,399 per month.
Figetz's variable cost = $45.00 x 25.75/100 = $11.59 per widget.
Bigby's variable cost = $45.00 x ( 25.75 - 3.50)/100 = $10.01 per widget

Last month, Bigby produced and sold 5,123 widgets. Figetz produced and sold 145 more widgets than Bigby.

Bigby's profit = 5,123 x ($45.00 - $10.01) - $101,900 = $77,354
Figetz's profit = (5,123 + 145) x ($45.00 - $11.59) - $80,399 = $95,605

Who made more profit and what was the % difference from the manufacturer who made the lower profit?

Figetz earned 23.6% more profit than Bigby: ($95,605 - $77,354) / $77,354 x 100%

Contest #12

2011-10-04T08:06:00.002-07:00

Solution to Contest #11

2011-10-04T07:53:00.002-07:00

Adam is an accountant. His client wants him to use this depreciation schedule for a certain asset:

In the first year, the asset is depreciated 20% from its original price. In subsequent years, the asset is depreciated by 8% of its book value.

What is the book value of a $109,000 asset after its fourth year?

The asset is bought for $109,000. In its first year, the depreciation is $109,000 x 0.20 = $21,800. The book value of asset is $109,000 - $21,800 = $87,200.

In the second year, the depreciation is $87,200 x 0.08 = $6,976. The book value of asset is $87,200 - $6,976 = $80,224.

In the third year, the depreciation is $80,224 x 0.08 = $6,418. The book value of asset is $80,224 - $6,418 = $73,806.

In the fourth year, the depreciation is $73,806 x 0.08 = $5,904. The book value of asset is $73,806 - $5,904 = $67,566.

So the correct answer is $67,902.

Contest #11

2011-09-03T07:59:00.003-07:00

Solution to Contest #10

2011-09-03T07:52:00.002-07:00

Bill is a sales representative for a farm equipment dealership. He gets paid $3,000 a month plus one half of a percent of tractor sales over $150,000 a month. Last month, Bill sold eight tractors for a total of $702,000. How much did the dealership pay Bill for the month?

Bill's base salary is $3,000 per month, and he earns this amount regardless of how much he sells. On the first $150,000 of sales, Bill earns no commission, but commission starts accumulating after this amount. All this can be translated into this equation:

Bill's monthly pay = $3,000 + ($702,000 - $150,000) x 0.5 / 100 = $5,760.

Contest #10

2011-08-01T07:33:00.003-07:00

Solution to Contest #9

2011-08-01T07:12:00.003-07:00

This is a two-step problem as the price of the dress is discounted twice.

Sara is an assistant manager in a clothing store. Her boss told her it is time to unload last year's fashions. He told her to reduce prices of all clothes by 25%. One red dress normally sells for $299.00.

The first discount is calculated as:

Discounted price = $299.00 x (1 - 0.25) = $224.25

It did not sell. So the boss told Sara to reduce the discounted price by 25%. What is the sale price of this dress?

The key word is "discounted." This tells us the reference for the second discount is based on the discounted price, not the original price.

Second discounted price = $224.25 x (1 - 0.25) = $168.18.

If the second discount had been stated as "So the boss told Sara to reduce the price by 25%," it would have been unclear whether the discount was to be applied to the original price (which would have given us $149.50 as the correct answer) or the discounted price. Even native speakers would be divided as to how to correctly translate this English phrase into math. Sometimes it is best to ask questions when then the "numbers English" seems a little too complicated.

Contest #9

2011-07-06T20:06:00.002-07:00

Sara is an assistant manager in a clothing store. Her boss told her it is time to unload last year's fashions. He told her to reduce prices of all clothes by 25%.

One red dress normally sells for $299.00. It did not sell. So the boss told Sara to reduce the discounted price by 25%. What is the sale price of this dress?

Show how the English is framing the calculations to get the right answer.

Solution to Contest #8

2011-07-06T19:52:00.002-07:00

Jack has two bank accounts that total $1,041.50.

x = first bank account, y = second bank account

x + y = 1,041.50

The first bank account has 35.1% less money than the second bank account.

x = y * (1 - 0.351) = y * 0.649

Solving:

y * 0.649 + y = 1,041.50

1.649 * y = 1,041.50

y = 631.50

So x = 1,041.50 - 631.60 = 409.90

What is the difference between the first and second bank account?

631.60 - 409.90 = 221.70

The difference between the two bank accounts is $221.70. Did you understand how the English formulated these calculations?

If the question was rephrased "The second bank account had 35.1% more money than the first," would the answer be different?

Contest #8

2011-06-04T09:11:00.002-07:00

Jack has two bank accounts that total $1,041.50. The first bank account has 35.1% less money than the second bank account.

What is the difference between the first and second bank account?

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Solution to Contest #7

2011-06-04T08:55:00.002-07:00

Jack bought 120 shares of ABC Banking for $12.27 each. He sold the shares 90 days later for 21.48% more than he paid. When he held the shares, ABC Bank paid a dividend of $0.55 per share. Brokerage fees are $25 or 0.5% of transaction amount, whichever is higher.

How much profit did Jack make with this investment?

Original Investment

Share Investment = 120 x $12.27 = $1,472.40

Brokerage Fees = $1,472.40 x 0.005 = $7.36. Since this was less than $25.00, the $25.00 fee was charged.

Total Investment = $1,472.40 + $25.00 = $1,497.40

Proceeds of Sale

Share price at sale = $12.27 x 1.2148 = $14.91

Total Sale Proceeds = $14.91 x 120 = $1,789.20

Brokerage Fees = $1,789.20 x 0.005 = $8.95. Since this was less than $25.00, the $25.00 fee was charged.

Total Proceeds of Sales = $1,789.20 - $25.00 = $1,764.20

Gain on Sales = $1,764.20 - $1,497.40 = $266.80

Dividends Paid = 120 x $0.55 = $66.00

Total Profit = $266.80 + $66.00 = $332.80

Contest #7

2011-05-01T06:08:00.004-07:00

Answers for Contest #6

2011-05-01T06:01:00.003-07:00

Jack, Fred, and Sara have $3000.
When this sentence is translated from English to math, the equation is:

J + F + S = 3000

Fred has a quarter the money that Jack has.

F = 1/4 x J

Sara has ten times as much money as Fred.

S = 10 x F

How much money does Jack have?

J + F + S = 3000

J + 1/4 x J + 10 x F = 3000

5/4 x J + 10 x (1/4 x J) = 3000

1.25J + 2.50J = 3000

3.75J = 3000

J = 800

Jack has $800.

Contest #6

2011-04-03T08:49:00.002-07:00

Jack, Fred, and Sara have $3000. Fred has a quarter the money that Jack has. Sara has ten times as much money as Fred. How much money does Jack have?

You can receive updates of this contest by subscribing to “DVBEupdate” on Twitter or by being a fan of “Dave Volek’s Business English” on Facebook.

Solution to Contest #5

2011-04-03T08:38:00.004-07:00

A number times the number less four is 320.

Here is the English to math translation:

"a number" becomes = "N"
"times" becomes = "x"
"less four" becomes "-4"
"is" becomes "="
"320" becomes "320"

So the direct translation becomes:

N x (N-4) = 320

When we solve, we get N = 20

Contest #5

2011-03-06T09:10:00.003-07:00

The math for Contest #4 must have been too hard for business English learners, so I will make this contest easier.

A number times the number less four is 320.

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Solution to Contest #4

2011-03-06T08:59:00.003-07:00

Four into a number is the product of the square root of the number and two-and-a-half.

"Into" means "divide," but the order is reversed. So "four into a number" is translated into "x / 4"

"is" becomes "="

"product" means a multiplication

"Square Root" is the . . . . . (sorry, this blog does not have the symbol for the square root) SQR

"two-and-a-half" becomes "2.5"

So the English is translated into this equation:

x / 4 = sqr(x) * 2.5

If we clear the fraction (multiply both sides by 4), we get:

x = sqr(x) * 10

Squaring both sides:

x^2 = x *100

Divide both sides by "x":

x = 100

Contest #4

2011-02-04T09:11:00.002-07:00

The last contest must have been too easy because no one tried it. Let's make it harder!

Four into a number is the product of the square root of the number and two-and-a-half.

Have your English teachers ever taught you what "into" means in numbers English? Probably not! I guess you will have to figure this vocabulary out by yourself.

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Solution to Contest #3

2011-02-04T09:02:00.004-07:00

Two-thirds of a number is two from that number.

Here's the translation:
"Two-thirds" becomes "2/3"
"of" becomes "times"
"a number" becomes "x"
"is" becomes "="
"two" becomes "2"
"from" becomes "-"
"that number" becomes "x"

If we do a direct translation, we get:

2/3 times x = 2 - x

However, when we use the word "from" to indicate a subtraction, we have to reverse the order. (Have any of your English teachers ever taught you this?). So the equation is properly translated to:

2/3 times x = x - 2

The correct answer is 6.

Contest #3

2011-01-20T20:33:00.002-07:00

Two-thirds of a number is two from that number.

Too easy, you say? Try to make the translation!

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Answer to Contest #2

2011-01-20T20:23:00.002-07:00

The English can be translated into this equation:

x (a number) + (plus) 4x (four times that number) - (minus) x/4 (a quarter of that number) = (is) 19 (19)

x + 4x - x/4 = 19

4x + 16x - x = 76

19x = 76

x = 4

The math is much easier than the English. I have to teach native speakers how to make these kinds of translations. How good are you at translating English into math?

Contest #2

2010-09-05T10:41:00.004-07:00

A number plus four-and-a-half times that number minus a quarter of that number is 19. What is the number?

A winner will be announced a few days after the first correct answer.

You can receive updates of this contest by subscribing to “DVBEupdate” on Twitter or by being a fan of “Dave Volek’s Business English” on Facebook.

Contest #1 Results

2010-09-05T10:35:00.001-07:00

Congratulations to Abhishek Duggal of Hawaii who won DVBE’s first Numbers Contest.

Here is the solution:

Let x=first number,y=second number,z=third number
x+y+z=99
x=y ÷2 or y=2x
z=3y= 3(2x)=6x
x+2x+6x=99
9x=99
x=11

Do you see how English is translated into equations? The DVBE program gives you lots of practice with these translations.

Contest #1

2010-08-30T16:12:00.001-07:00

The sum of three numbers is 99. The first number is one-half the value of the second number. The third number is three times the second. What is the first number?

I will announce the winner around September 30, 2010.