SOLUTION: A painter needs to use white and green paint, in the ratio of 5:2, to mix 3 1/2 gallons. Determine amount (in quarts) of each. 3 1/2 gal. = 14 quarts (Converting to same units

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Question 1045753: A painter needs to use white and green paint, in the ratio of 5:2, to mix 3 1/2 gallons. Determine amount (in quarts) of each.
3 1/2 gal. = 14 quarts (Converting to same units of measure).
The amount of white is 5/2 of the amount of green.
5x + 2x = 14
7x = 14
x = 2
5(2) + 2(2) = 14
10 + 4 = 14
Where am I correct?
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Yes 14 quarts.

w, quarts of white paint
g, quarts of green paint


w%2Fg=5%2F2, but be careful accounting for the total parts to make the 14 quarts.


The mixture according to ratio is 5 parts white plus 2 parts green making 5+2=7 parts PAINT MIXTURE.
The FRACTION as white is 5%2F7.
The FRACTION as green is 2%2F7.


Look at accounting for the 14 quarts of mixture.
w%2Bg=14.


What equations do you now have so far? The EQUATIONS!
system%28w%2Fg=5%2F2%2Cw%2Bg=14%29
That's all.
One ratio equality and one volume accounting.
Two equations in only two unknown variables.
This did not actually apply the "7 parts as paint mixture" discussion.


SOLVING THE SYSTEM
-
w=5g%2F2
-
%285g%2F2%29%2Bg=14
5g%2B2g=2%2A14
7g=28
g=28%2F7
highlight%28g=4%29
-
w=5g%2F2
w=5%2A4%2F2
highlight%28w=10%29

Same results, but maybe easier to understand.

Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
A painter needs to use white and green paint, in the ratio of 5:2, to mix 3 1/2 gallons. Determine amount (in quarts) of each.
3 1/2 gal. = 14 quarts (Converting to same units of measure).
The amount of white is 5/2 of the amount of green.
5x + 2x = 14
7x = 14
x = 2
5(2) + 2(2) = 14
10 + 4 = 14
Where am I correct?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Your solution is correct.


Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

A painter needs to use white and green paint, in the ratio of 5:2, to mix 3 1/2 gallons. Determine amount (in quarts) of each.
3 1/2 gal. = 14 quarts (Converting to same units of measure).
The amount of white is 5/2 of the amount of green.
5x + 2x = 14
7x = 14
x = 2
5(2) + 2(2) = 14
10 + 4 = 14
Where am I correct?
Perfect!! You're right! Very simple and correct. You did get 10 quarts of white and 4 quarts of green. Again, good job!

By the way, you don't have to even look at the other solution from the other person because your solution was simple and to the point,

just the way it should be.