A commercial bakery uses flour, sugar, and cocoa powder in a weight ratio of 5 : 3 : 2 to … — ACT

A commercial bakery uses flour, sugar, and cocoa powder in a weight ratio of $5 : 3 : 2$ to make a chocolate cake base. To create a specialty low-sugar version, the baker decreases the amount of sugar by $30\%$ and adds that exact reduced weight to the flour, leaving the amount of cocoa powder unchanged. What is the ratio of flour to sugar in the new specialty batch?

A
$50 : 21$
$59 : 21$ Answer
C
$59 : 100$
D
$65 : 21$
E
$53 : 27$

Answer

The ratio of flour to sugar in the new specialty batch is

59 : 21

In the original ratio

5 : 3 : 2

, sugar accounts for

3

ratio units. Decreasing sugar by

30\%

removes

30\% \text{ of } 3 = 0.9

units, leaving

3 - 0.9 = 2.1

units of sugar. Adding those

0.9

units to the original

5

units of flour increases flour to

5 + 0.9 = 5.9

units. The ratio of new flour to new sugar is

5.9 : 2.1

, which multiplies by

10

to yield

59 : 21

Step-by-Step Solution

Determine the initial ratio units for each component.

Flour =

5

units, Sugar =

3

units, Cocoa =

2

units.

The original weight ratio given is

5 : 3 : 2

Calculate the reduction in sugar and the new sugar ratio amount.

Reduction =

3 \times 0.30 = 0.9

units; New Sugar =

3 - 0.9 = 2.1

units.

Sugar is reduced by

30\%

of its original proportion.

Add the removed weight to the flour to find the new flour ratio amount.

New Flour =

5 + 0.9 = 5.9

units.

The weight subtracted from sugar is added directly to the flour.

Form the new ratio of flour to sugar and simplify to whole numbers.

5.9 : 2.1 = 59 : 21

Multiplying both parts of the decimal ratio

5.9 : 2.1

10

converts it into a simple integer ratio.

Key Concept

Adjusting part-to-part ratios by applying percentage changes to individual components and simplifying fractional ratios.

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