A painter is mixing a custom green paint. The formula requires mixing blue and yellow pain… — Armed Services Vocational Aptitude Battery (ASVAB)

A painter is mixing a custom green paint. The formula requires mixing blue and yellow paint in a ratio of $1$ part blue to $3$ parts yellow. He needs exactly $22\frac{1}{2}$ gallons of the green paint mixture for a large commercial job. So far, he has poured $1\frac{3}{4}$ gallons of blue paint from one can, and $2$ quarts of blue paint from another can into the mixing bucket. How many more gallons of blue paint does he need to add to reach the correct amount of blue paint for the entire job?

$3\frac{3}{8}$ Answer
B
$5\frac{1}{4}$
C
$3\frac{23}{24}$
D
$1\frac{7}{8}$

Answer

The painter needs

3\frac{3}{8}

more gallons of blue paint.

First, the correct fraction of blue paint is identified from the

1:3

ratio, which is

1

part out of

4

total parts (

\frac{1}{4}

). The total blue paint needed is

\frac{1}{4}

22\frac{1}{2}

gallons, which is

5\frac{5}{8}

gallons. The painter has already poured

1\frac{3}{4}

gallons and

2

quarts (which is

\frac{1}{2}

gallon). Adding these gives

2\frac{1}{4}

gallons poured. Finally, subtracting the poured amount from the total needed (

5\frac{5}{8} - 2\frac{1}{4}

) leaves

3\frac{3}{8}

gallons.

Step-by-Step Solution

Determine the fraction of the mixture that is blue paint.

The ratio of blue to yellow is

1:3

, meaning there is

1

part blue for every

4

total parts (

1 + 3

). The fraction is

\frac{1}{4}

This is necessary to find out how much blue paint is required for the entire

22\frac{1}{2}

gallon mixture.

Calculate the total amount of blue paint needed for the job.

\frac{1}{4} \times 22\frac{1}{2} = \frac{1}{4} \times \frac{45}{2} = \frac{45}{8} = 5\frac{5}{8}

gallons.

Multiplying the total mixture volume by the fraction of blue paint gives the target amount of blue paint.

Convert the quarts of blue paint already poured into gallons.

Since

4

quarts equal

1

gallon,

2

quarts is equal to

\frac{2}{4}

\frac{1}{2}

gallon.

All measurements must be in the same unit (gallons) before adding them together.

Calculate the total amount of blue paint already poured.

1\frac{3}{4} + \frac{1}{2} = 1\frac{3}{4} + \frac{2}{4} = 1\frac{5}{4} = 2\frac{1}{4}

gallons.

This finds the combined volume of the two separate pours of blue paint.

Subtract the poured amount from the total needed amount.

5\frac{5}{8} - 2\frac{1}{4} = 5\frac{5}{8} - 2\frac{2}{8} = 3\frac{3}{8}

gallons.

Subtracting what has been poured from the target amount gives the remaining amount needed.

Key Concept

Fraction addition and subtraction in practical measurement scenarios, including basic unit conversion and proportional reasoning.

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