Question

You mix 1/2 quart of blue paint for every 1/3 quart of red paint to make 5 quarts of purple paint. How much blue paint and how much red paint do you use?

Answer 1

3 quarts of blue paint and 2 quarts of red paint

Explanation:

Let

x ---> quarts of blue paint

y ---> quarts of red paint

we know that

You make 5 quarts of purple paint

so

`x+y=5` ----> equation A

The ratio of of blue paint to red paint is

`(x)/(y) =((1/2))/((1/3))`

`(x)/(y)=1.5`

`x=1.5y` ----> equation B

Solve the system by substitution

substitute equation B in equation A

`1.5y+y=5`

solve for y

`2.5y=5\\y=2`

Find the value of x

`x=1.5(2)=3`

therefore

3 quarts of blue paint and 2 quarts of red paint