A brownie recipe asks for three and one third times as much sugar as chocolate chips. If one and one quarter cups of sugar is used, what quantity of chocolate chips would then be needed, according to the recipe?
Question
A brownie recipe asks for three and one third times as much sugar as chocolate chips. If one and one quarter cups of sugar is used, what quantity of chocolate chips would then be needed, according to the recipe?
Solution
To solve this problem, we need to set up a proportion. The problem tells us that the recipe uses three and one third times as much sugar as chocolate chips. This can be written as 3 1/3 : 1.
The problem also tells us that 1 1/4 cups of sugar is used. We can set this equal to 3 1/3 and solve for the unknown quantity of chocolate chips.
First, convert the mixed numbers to improper fractions. 3 1/3 becomes 10/3 and 1 1/4 becomes 5/4.
So, we have the proportion 10/3 : 1 = 5/4 : x.
Cross-multiply to solve for x:
10/3 * x = 5/4
Multiply both sides by the reciprocal of 10/3, which is 3/10, to isolate x:
x = 5/4 * 3/10
Simplify the right side to find x:
x = 15/40
Simplify the fraction to lowest terms:
x = 3/8
So, according to the recipe, 3/8 cup of chocolate chips would be needed.
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