Question

Leo spent the same amount of time working on each of 5 different weight machines and then spent 2/3 of an hour on the treadmill. If he spent a total of 1 3/4 hours at the gym, which shows the correct equation and solution for x, the number of hours Leo spent at each of the weight machines?

Answer 1

Let us say that the variable x is the amount of number of hours Leo spent at each of the weight machines.

Since there are 5 machines, therefore = 5 x

Adding this variable to the number of hours spent on the treadmill will give the total number of hours Leo spent at the gym. That is:

5 x + 2 / 3 = 1 3 / 4

5 x + 2 / 3 = 7 / 4

Therefore the correct equation is:

5 x + 2 / 3 = 7 / 4

Or if no denominator, we multiply the whole equation with 12 so that:

(5 x + 2 / 3 = 7 / 4) * 12

60 x + 8 = 21

or

60 x = 13

 

Solving for x will give:

x = 13 / 60

x = 0.217 hours

Leo spend 0.217 hours on each of the 5 machines.

Answer 2

Let's break this down. We know that there are 5 weight machines, and Leo spent an equal amount of time on all of them. Since we don't know how long he spent on each, we'll use x. Our equation so far is 5x. Then, we know that he spent 2/3 hour on the treadmill, which we will just add to the 5x. So, now our equation is 5x + 2/3. Lastly, we know that the total time Leo spent at the gym is 1 3/4 hours, which we set the last equation equal to. Our final equation is 5x + 2/3 = 1 3/4. Then, all we have to do is solve for x. What we can do to make this easier is to change all of the fractions into numbers. After changing everything, here is our equation: 5x + 40 = 105. Then, we will subtract 40 from each side and divide both sides by 5. Therefore, Leo spent 13 minutes on each weight machine.

ANSWER:

A) 5x + 2/3 = 1 3/4 ; Leo spent 13 minutes at each machine

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