To make a specific shade of green paint, a painter mixes yellow paint and blue paint in a … — SAT

To make a specific shade of green paint, a painter mixes yellow paint and blue paint in a ratio of $3$ to $5$ . If the painter wants to make a total of $40$ gallons of this green paint, how many gallons of yellow paint are needed?

A
$12$
$15$ Answer
C
$24$
D
$25$

Answer

The correct amount of yellow paint needed is

15

gallons.

The correct answer is

15

gallons. Since the ratio of yellow to blue paint is

3:5

, the total mixture consists of

3 + 5 = 8

equal parts. Yellow paint represents

3

of these

8

parts, or

\frac{3}{8}

of the total mixture. To find the amount of yellow paint needed for

40

gallons of green paint, multiply the fraction by the total volume:

\frac{3}{8} \times 40 = 15

gallons.

Step-by-Step Solution

Determine the fraction of the total mixture that is yellow paint.

The ratio of yellow to blue paint is

3:5

, which gives a total of

3 + 5 = 8

parts. Therefore, yellow paint represents

\frac{3}{8}

of the total mixture.

To find the amount of one component in a given total volume, we must find the part-to-whole ratio of that component to the total mixture.

Multiply the fraction representing yellow paint by the total desired volume of green paint.

\frac{3}{8} \times 40 = 3 \times 5 = 15

gallons.

Multiplying the part-to-whole ratio by the total volume gives the specific volume of yellow paint needed.

Key Concept

Solving part-to-whole ratio problems by summing the ratio parts to find the total parts, then multiplying the corresponding fraction by the total quantity.

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