Paint costing $19 per gallon is to be mixed with thinner costing $3 per gallon. How much of each should be added to make 16 gallons of a mix that costs $14 per gallon?

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23-09-2017
Mathematics

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Paint costing $19 per gallon is to be mixed with thinner costing $3 per gallon. How much of each should be added to make 16 gallons of a mix that costs $14 per gallon?

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amysmithiscool amysmithiscool · Answer 1 · 2017-09-23T19:21:19+02:00

amysmithiscool amysmithiscool

23-09-2017

let x represent gallons of $19 paint
let y represent gallons of $3 paint

first you make your 2 equations

x+y=16, y=16-x
(19x+3y) ÷ 16 = 14

then you use substitution

14 = (19x + 3(16-x) ) ÷16
224 = 19x + 48 - 3x
176 = 16x
11 = x, so there's 11 gallons of $19 paint
recall that x+y=16
11+y=16
5=y

so there are 11 gallons of $19 paint and 5 gallons of $3 paint

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