Purple paint is made with 16:3:1 ratio of white paint: blue paint :red paint. How much white paint in gallons is needed in order to make one gallon of purple paint? Express your answer as a common fraction.
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OpenStudy (anonymous):
Will give a medal and fan who ever helps
jimthompson5910 (jim_thompson5910):
"Purple paint is made with 16:3:1 ratio of white paint: blue paint :red paint"
so we have
16x gallons of white paint
3x gallons of blue paint
1x gallons of red paint
they all mix to get purple. The variable x is some unknown number at this point
jimthompson5910 (jim_thompson5910):
they mix to make 1 full gallon, so
16x + 3x + 1x = 1
solve that for x and then evaluate 16x to get your answer
OpenStudy (anonymous):
Thank you so much for helping
jimthompson5910 (jim_thompson5910):
no problem
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OpenStudy (anonymous):
Would that be 18 then?
jimthompson5910 (jim_thompson5910):
16x + 3x + 1x = 1
20x = 1
x = ???
OpenStudy (anonymous):
oh
OpenStudy (anonymous):
sorry it's just im a slow learner
jimthompson5910 (jim_thompson5910):
thats fine
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jimthompson5910 (jim_thompson5910):
if 20x = 1, then what is x?
OpenStudy (anonymous):
um 20x=1 so
-20 -20
x=-19
jimthompson5910 (jim_thompson5910):
you don't subtract 20 from both sides
jimthompson5910 (jim_thompson5910):
20x means 20 times x
so you have to do the opposite of multiplication
OpenStudy (anonymous):
oh
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OpenStudy (anonymous):
I'm sorryy
OpenStudy (anonymous):
so then 20x=1
/20
x=1
jimthompson5910 (jim_thompson5910):
you divide BOTH sides by 20 though
jimthompson5910 (jim_thompson5910):
not just that left side
OpenStudy (anonymous):
oh Sorryyy T-T
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OpenStudy (anonymous):
20x=1
/20 /20
x=.05
jimthompson5910 (jim_thompson5910):
correct
so x = 1/20 or x = 0.05
jimthompson5910 (jim_thompson5910):
you use this x value to compute 16x to get your final answer
OpenStudy (anonymous):
Ohh ok
jimthompson5910 (jim_thompson5910):
it says "Express your answer as a common fraction"
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OpenStudy (anonymous):
So then you would get 0.8? which is 80/100
jimthompson5910 (jim_thompson5910):
so you will have to stick with x = 1/20
OpenStudy (anonymous):
oh
jimthompson5910 (jim_thompson5910):
reduce all fractions
jimthompson5910 (jim_thompson5910):
0.8 = 80/100 = ???
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OpenStudy (anonymous):
4/5
jimthompson5910 (jim_thompson5910):
yep
jimthompson5910 (jim_thompson5910):
you'll need 4/5 of a gallon of white paint
OpenStudy (anonymous):
Thank you so much for helping me and dealing with my slowness