Question

2. Susan wants to use blue, yellow, green, and pink paint to decorate her house. She needs 3 times as much blue paint as yellow paint and ½ much yellow paint as green paint. She needs 3 ¼ gallons of pink paint, which is ¾ of a gallon more than the green paint she needs. How much paint does Susan need in all?

Answer 1

B = Blue

Y = Yellow

G = Green

P = Pink

The info that we have is:

3*B = Y

(1/2)Y = G

P = (3 + 1/4) gal

P = G + 3/4 gal.

So we have 4 equations. The first step is replacing the third equation into the fourth equation, and get:

G + 3/4 gal = (3 + 1/4) gal

G = (3 + 1/4) gal - 3/4 gal = (2 + 2/4) gal

Now we can replace this into the second equation ((1/2)*Y = G) to find the value of Y.

(1/2)Y = (2 + 2/4) gal

Y = 2*(2 + 2/4) gal = (4 + 1)gal = 5 gal.

Now we can replace this into the first equation and get:

3*B = 5gal

B = 5/3 gal = (1 + 2/3)gal

So the total amount of paint used is:

T = P + G + Y + B = (3 + 1/4) gal + (2 + 2/4) gal + 5gal + (1 + 2/3)gal

T = (11 + 3/4 + 2/3)gal

T = (11 + 9/12 + 8/12)gal = (11 + 17/12)gal = (11 + 1 + 5/12)gal = (12 + 5/12) gal.