pg.169 #38 7th grade math book

Question

You mix 2/5 cups of red paint for every 1/4 cup of blue paint to make 1 5/8 gallons of purple paint.

 

A. How much red paint and blue paint do you use?

 

B. You decide you want to make lighter purple paint. You make the new mixture by adding 1/10 of white paint for every 2/5 cup of red paint and 1/4 cup of blue paint. How much red paint, blue paint, and white paint do you use to make 3/8 gallon of lighter purple?

Answer 1

A) 4 quarts=1 gallon

1 5/8 gallons=(1 5/8)(4)=52/8=6.5 quarts

1 quart=4 cups

6.5 quarts=6.5*4=26 cups

1 5/8 gallons=26 cups

(2/5)(x)+(1/4)(x)=26

(8/20)(x)+(5/20)(x)=26

(13/20)(x)=26

multiply both sides by (20/13)

(20/13)(13/20)(x)=(20/13)(26)

x=40

40(2/5)=16 cups of red paint (4 quarts)

40(1/4)=10 cups of blue paint (2.5 quarts)

 

B) (3/8)(4)=12/8=1.5 quarts

1.5*4=6 cups

(1/10)(x)+(2/5)(x)+(1/4)(x)=6

(2/20)(x)+(8/20)(x)+(5/20)(x)=6

(15/20)(x)=6

(3/4)(x)=6

(4/3)(3/4)(x)=(4/3)6

x=8

8*(1/10)=8/10=4/5 cup white paint

8*(2/5)=16/5=3 1/5 cups red paint

8*(1/4)=2 cups blue paint