A petroleum company has two different sources of crude oil. The first source provides crude oil that is 70% hydrocarbons, and the second one provides crude oil that is 95% hydrocarbons. In order to obtain 160 gallons of crude oil that is 80% hydrocarbons, how many gallons of crude oil must be used from each of the two sources?
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let x = gallons of 70% mixture
let y = gallons of 95% mixture
x + y = 160
y = 160 - x
.7x + .95y = .8(x + y)
.7x + .95(160 - x) = .8 * 160
.7x + 152 - .95x = 128
-.25x = -24
x = 96 gallons
y = 64 gallons
let y = gallons of 95% mixture
x + y = 160
y = 160 - x
.7x + .95y = .8(x + y)
.7x + .95(160 - x) = .8 * 160
.7x + 152 - .95x = 128
-.25x = -24
x = 96 gallons
y = 64 gallons