Question

Shelly has an incomplete recipe of a dish. She knows that for every 7 cups of flour, she should add 2 cups of butter, and for every 3 cups of butter, she should add 2 cups of sugar. If the dish Shelly is cooking requires 5 cups of flour, how many cups of sugar would she need?

• A. $\frac{20}{21}cups$
• B. $\frac{21}{20}cups$
• C. $1cup$
• D. $\frac{1}{2}cups$

Answer 1

The correct option is A $\frac{20}{21}cups$

Listing the ratios given, we get:

$Flour:Butter=7:2Butter:Sugar=3:2$

Multiplying both sides of the first ratio by 3 and those of the second ratio by 2, we get:

$Flour:Butter=7\times 3:2\times 3=21:6Butter:Sugar=3\times 2:2\times 2=6:4$

So, for 21 cups of flour, the recipe uses 6 cups of butter and 4 cups of sugar.

$⟹Flour:Butter:Sugar=21:6:4$

Dividing each part of the ratio by 21, we get:

$Flour:Butter:Sugar=\frac{21}{21}:\frac{6}{21}:\frac{4}{21}=1:\frac{2}{7}:\frac{4}{21}$

Multiplying each part of the ratio by 5, we get:

$Flour:Butter:Sugar=5\times 1:5\times \frac{2}{7}:5\times \frac{4}{21}=5:\frac{10}{7}:\frac{20}{21}$

Hence, for 5 cups of flour, the amount of sugar required is $\frac{20}{21}cups.$