# Thread: Stuck on this word problem !! Appreciate the Help !

1. ## Stuck on this word problem !! Appreciate the 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 3 liters of paint which is half blue and half yellow.

2. ## Re: Stuck on this word problem !! Appreciate the Help !

Hint:
b:y canA = 9:1
b:y canB = 1:4
b:y can(A+B) = 10:5

3. ## Re: Stuck on this word problem !! Appreciate the Help !

after mixing you want 1.5 liters of both blue and yellow

so we're looking for quantities $x_1,~x_2$ such that

$(0.9)x_1 + (0.2)x_2 = 1.5$

$(0.1)x_1 + (0.8)x_2 = 1.5$

subtract the 2nd equation from the first

$(0.8)x_1 - (0.6)x_2 = 0$

$(0.8)x_1 = (0.6)x_2$

$x_2 = \dfrac 4 3 x_1$

plug this back into equation 1

$(0.9)x_1 + (0.2)\left(\dfrac 4 3 x_1\right) = 1.5$

$\left(\dfrac{9}{10} + \dfrac{8}{30}\right)x_1 = \dfrac 3 2$

$\dfrac{35}{30}x_1 = \dfrac 3 2$

$x_1 = \dfrac{90}{70} = \dfrac{9}{7} ~liter$

$x_2 = \dfrac 4 3 x_1 = \dfrac{12}{7}~liter$

4. ## Re: Stuck on this word problem !! Appreciate the Help !

Let "X" be the number of liters you use from can A and let "Y" be the number of liters you use form can B. Since can A "has 9 parts of blue paint to one part of yellow paint" that gives 0.9X liters of blue and 0.1X liters of yellow (9 parts and 1 part total 10 parts. "9 parts" is 9/10= 0.1 and 1 part is 1/10= 0.1). Since can B "is 20 percent blue paint and the rest is yellow paint" that gives 0.2Y liters of blue and 0.8Y liters of yellow. That is a total of 0.9X+ 0.8Y blue and 0.1X+ 0.8Y yellow.

We want a total of "3 liters of paint" so X+ Y= 3. We want " half blue and half yellow" so 0.9X+ 0.1Y= (X+ Y)/2= 3/2= 1.5 and 0.2X+ 0.8Y= (X+ Y)/2= 3/2= 1.5. That appears to be three equations for two unknowns but, since the percentages must add to 100% the last two automatically give "X+ Y= 3". Multiply 0.9X+ 0.1Y= 1.5 by 0.8 to get 0.72X+ 0.08Y= 1.2. Multiply 0.9X+ 0.1Y= 1.5 by 0.1 to get 0.09X+ 0.08Y= 0.15. Subtract the second equation from the first: 0.81X= 1.05. Divide both sides by 0.81 to get X= 1.30 (to two decimal places). Y= 3- 1.30= 1.70.

So you want 1.30 liters of A and 1.70 liters of B. That is, of course a total 0f 3.00 liters. A is 9/10 blue and B is 20% blue that is a total of (0.9)(1.3)+ (0.2)(1.7)= 1.51 liters of blue and 1.49 liters of yellow. The discrepancy (not 1.5 and 1.5) is due to rounding.