SOLUTION: How much fuel that sells for $1.25 per gallon must be mixed with 180 gallons that sells for $2.00 per gallon to obtain a mixture that sells for $1.55 per gallon? i've tried: X

Question 94404: How much fuel that sells for $1.25 per gallon must be mixed with 180 gallons that sells for $2.00 per gallon to obtain a mixture that sells for $1.55 per gallon?
i've tried:
X = amount of fuel added
1.25X+(2.00)(180-X)= (1.55)(180)
1.25X+360-2.00X=279
-.75X=-81
X=108
Answer by kev82(151) (Show Source): You can put this solution on YOUR website!
Hi,

Firstly, I'd like to say it was great to see you've had an attempt. that's not really normal on this site.

It seems like you have the right idea by considering the amounts and concentrations(well prices) but you've got the amounts a bit wrong. I'll look at your equation in 3 parts:

The first thing you say is 1.25X. This is X gallons at a price of $1.25 I'm happy with that, because the probelm says "How much fuel that sells for $1.25 per gallon"

Then you add (2.00)(180-X). This I don't understand. Here you are saying the amount of $2.00 fuel you put in is 180-X which is 180 minus the amount of $1.25 fuel you put in. This is not what the question says It says "must be mixed with 180 gallons that sells for $2.00 per gallon". It doesn't matter what X is, we always add 180 gallons of the stuff. So this should be 2(180)

The final part (1.55)(180) is also wrong, if you take X gallons of $1.25 fuel, and 180 gallons of $2.00 fuel, then how many gallons of fuel do you have in total? 180+X right?

So you should have the equation 1.25X + 2*180 = 1.55(180+X). Solving that should give you the correct answer, I'll leave the rest to you.

Kev
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