Question

A middle school basketball game includes 32 minutes of playing time. What percent of the game has passed when the time remaining is one third of the time played so far?
Please help

Answer 1

Im not sure, but I believe the answer is 24 because 8x4=32. But 8x the third is 24.

Answer 2

Think of it this way—

It’s easiest to set up an equation to represent the entire timespan of the game.

x can represent the time played so far.
We already know that 32 is the total time of the game, so therefore:

32 = x + 1/3x

All we have to do from here is solve for x.

We can combine the 2 x values because they are like terms, as long as their fractions both have the same denominator:

x + 1/3x = 3/3x + 1/3x = 4/3x

Now we have:

32 = 4/3x

Now just multiply both sides by 3/4, because that will cancel out the fraction on the right side which will isolate x:

3/4(32) = x

3/4 times 32 is 24, so x is equal to 24.

The question asks for the PERCENT, so we must find that using our answer and the total game time.

24 divided by 32 is .75, times 100 is 75.

The final answer is 75%.