# "Cans of Paint" Word Problem

• Oct 13th 2009, 09:32 PM
Togechu64
"Cans of Paint" Word Problem
Hey guys, this problem has been giving me a headache for the last hour, and its the last problem I need to do before my homework is due in an hour and a half! Help!

I have two cans of paint. Can A has 9 parts of blue paint to one part of yellow paint. Can B is 20 percent blue paint and the rest is yellow paint. How much paint should I use from each can to obtain 2 liters of paint which is half blue and half yellow.

amount of can A= ___________________ liters
amount of can B= ___________________ liters
• Oct 13th 2009, 09:48 PM
Togechu64
(Crying)

The farthest I keep getting is that A + B= 2L, but I have no idea what other equation to set up, I've tried a bunch.
• Oct 13th 2009, 10:14 PM
earboth
Quote:

Originally Posted by Togechu64
Hey guys, this problem has been giving me a headache for the last hour, and its the last problem I need to do before my homework is due in an hour and a half! Help!

I have two cans of paint. Can A has 9 parts of blue paint to one part of yellow paint. Can B is 20 percent blue paint and the rest is yellow paint. How much paint should I use from each can to obtain 2 liters of paint which is half blue and half yellow.

amount of can A= ___________________ liters
amount of can B= ___________________ liters

1. Can A: $\displaystyle \frac9{10}$ blue + $\displaystyle \frac1{10}$ yellow

Can B: $\displaystyle \frac2{10}$ blue + $\displaystyle \frac8{10}$ yellow

2. Let x denote the amount of cans A and y the amount of cans B. Of each color you need exactly 1 litre.

3. Solve the system of equations for x, y:

$\displaystyle \left|\begin{array}{rcl} \frac{9}{10} x + \frac{2}{10} y &=& 1 {\color{blue}\bold{blue}}\\ \frac{1}{10} x + \frac{8}{10} y &=& 1 {\color{yellow}\bold{yellow}}\end{array}\right.$

Spoiler:
I've got $\displaystyle x = \frac67~\vee~y=\frac87$
• Oct 13th 2009, 10:21 PM
Togechu64
PERFECT!!! I worked it out and got exactly the right answer, thank you so much, you're an incredible life saver! I've made sure to write down your explanation so I have a practice problem to review for the midterm, thank you very much again for all your help!!!(Rofl)