Question in description

Question

 

When the mechanic at a car dealership checked the cars on the lot, he found that some were ½ full of gas and some were ¼ full. There were a total of 85 cars and 30 tanks of gas in all. All of the cars have the same size gas tank. How many cars were ½ full?

Answer 1

h = number half full cars

q = number quarter full cars

 

h + q = 85     since there are 85 cars

 

(1/2)(number half full) + (1/4)(number quarter full) = 30 tanks

h/2 + q/4 = 30

 

Multiply 2nd equation through by 4 to clear fractions:

2h + q = 120

 

2h + q = 120

  h + q = 85      subtract

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h = 35 cars half full

 

This leaves 50 cars quarter full

 

50(1/4) + 35(1/2) = 12.5 + 17.5 = 30 tanks