Question

Reid and his workout partner are lifting weights together, doing many sets of each exercise. On a certain exercise, Reid is using a 23-pound bar, increasing the amount of weight he lifts by 3 pounds on each set. His partner, meanwhile, started out using a 35-pound bar and is upping the weight by adding 1 pound on every set. Eventually, Reid and his workout partner will be lifting the same amount, and will take turns using the same barbell. How many sets will they have completed? How much weight will they be lifting then?

Answer 1

Let's denote the number of sets as \(n\).

Reid's weight for each set is \(23 + 3n\) pounds.

His workout partner's weight for each set is \(35 + 1n\) pounds.

When they are lifting the same amount, we can set up an equation:

23 + 3n = 35 + 1n

Combine like terms:

2n = 12

Solve for n:

n = 6

So, they will have completed 6 sets. To find the weight they will be lifting, substitute n back into either of the expressions:

Reid's weight for the 6th set: 23 + 3 times 6 = 23 + 18 = 41 pounds.

Workout partner's weight for the 6th set: 35 + 1 times 6 = 35 + 6 = 41 pounds.

Therefore, they will be lifting 41 pounds each, and they will have completed 6 sets. It's done there.