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. Last month, Bigby produced and sold 5,123 widgets. Figetz produced and sold 145 more widgets than Bigby.
Who made more profit and what was the % difference from the manufacturer who made the lower profit?
Tuesday, October 4, 2011
Solution to Contest #11
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.
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.
Saturday, September 3, 2011
Contest #11
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?
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?
Solution to Contest #10
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.
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.
Monday, August 1, 2011
Contest #10
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?
Solution to Contest #9
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.
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.
Wednesday, July 6, 2011
Contest #9
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.
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.
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