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when the mechanic at a at the car dealership checked the cars on the lot, he found that some were 1/2 full of gas and some were 1/4 full. There were a total of 85 cars but only enough gas to fill 30 tanks. All of the cars have the same size gas tank. How many cars were 1/2 full?

Let x=# of cars that are 1/2 full of gas, then 85-x=# of cars that are 1/4 full

Thus, (1/2)x + (1/4)(85-x) = 30 ... solving for x:

(1/2)x + 85/4 - (1/4)x = 30

(1/4)x = 30-85/4, now multiply by 4

x = 4(30-85/4)

= 120-85 = 35

35 cars were 1/2 full.

Abe

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Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Over 15 years teaching at the college level.**Organizations**

NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.**Education/Credentials**

B.S. in Mathematics from Rensselaer Polytechnic Institute

M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook