Question

A painter plans to paint a room with an area of 515 square feet. He mixes paint to create a specific shade of green. The ratio of each color in his mixture is shown:
- 1 part blue paint
- 3 parts yellow paint
- 2 parts white paint

Part A
The painter estimates that he will need 1 gallon of green paint for every 175 square feet of the room. He estimates the smallest number of whole gallons of green paint needed to paint the room. How much blue paint will the painter need to make this batch of green paint?

Part B
The painter makes a second batch of green paint using the same ratio of blue, yellow and white paint. He uses 3 gallons of white paint to make the second batch of green paint. How many total gallons is the second batch of green paint?

Part C
The painter purchases 6 gallons of paint on sale for $153.50. The regular price for the paint was $139.92 for 4 gallons. How many dollars per gallon did the painter save purchasing the paint on sale?

Part D
The painter mixes some extra green paint with red paint to make a batch of brown paint. The painter uses 3 parts of green paint for every 2 parts of red paint. He mixes a total of 2 gallons of brown paint. How many gallons of yellow paint are in this batch of brown paint?

Answer 1

Part A: 87.5 Gallons
Part B: 8 Gallons
Part C: $86.38
Part D: N/A

Answer 2

Answer:

Part A : 0.50 gallons of blue paint

Part B : 9 gallons of green paint

Part C : $9.40 per gallon

Part D : 0.6 gallon yellow paint

Step-by-step explanation:

A painter makes green paint by mixing

Blue paint = 1 part

Yellow paint = 3 parts

White paint = 2 parts

For 1 gallon of green paint he needs

Blue paint = 1/6 of 1 gallon = 0.17 gallon

Yellow paint = 3/6 of 1 gallon = 0.5 gallon

White paint = 2/6 of 1 gallon = 0.33 gallon

Part A:

175 square feet of the room needs green paint = 1 gallon

515 square feet of the room needs green paint = 515 ÷ 175 = 2.943 gallons

In 1 gallon of green paint, the amount of blue paint = 0.17 gallon

in 2.943 gallons of green paint, the amount of blue paint is = 2.943 × 0.17 = 0.50 gallons

Part B :

The painter uses 3 gallons of white paint to make green paint.

Let the total green paint be made x gallons

$\frac{2}{6}$ of x gallons = 3 gallons

x = 3 × $\frac{6}{2}$  = $\frac{18}{2}$ = 9 gallons

Part C :

The painter purchases 6 gallons of paint on sale for = $153.50

Per gallon price = $\frac{153.50}{6}$ = $25.58

The regular price was for 4 gallons = $139.92

per gallon regular price = $34.98

The painter saves per gallon = 34.98 - 25.58 = $9.40

Part D :

The painter mixes 2 gallons of brown paint.

For that he uses 3 parts of green paint = $\frac{3}{5}$ × 2 = 1.2 gallons

and 2 part of red paint = $\frac{2}{5}$ × 2 = 0.8 gallon

For 1.2 gallons green paint, he needs yellow paint = $\frac{3}{6}$ × 1.2 = 0.6 gallons