How would you write this word problem as an equation?
When the gas gauge on her car was at the \(\frac{3}{8}\) mark, Karen pumped 15 gallons of gas into the tank to fill it. How many gallons of gas does the tank in Karen's car hold?
Answer (2)
If the tank was 3/8 full, then it was 5/8 empty. It took 15 gallons to fill those empty 5/8 of a tank.
5/8 x (1 tank) = 15 gallons
1 tank = 15 / (5/8) = 15 x 8/5 = 24 gallons
The equation representing the word problem is 8 5 x = 15 , where x is the total capacity of the tank. By solving the equation, we find that the tank holds 24 gallons. This means that when the gauge was at 8 3 , Karen had 9 gallons of gas already in the tank before she added 15 gallons.
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