Question

Cody and his workout partner are lifting weights together, doing many sets of each exercise. On a certain exercise, Cody is using a 19-kilogram bar, increasing the amount of weight he lifts by 2 kilograms on each set. His partner, meanwhile, started out using a 20-kilogram bar and is upping the weight by adding 1 kilogram on every set. Eventually, Cody 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

In 1 set, they will be lifting the same weight.

They will be lifting the same weight when they are both lifting 21 kilograms.

Step-by-step explanation

Cody starts with 19 kilogram bar and increases this by 2 kilograms on each set.

In n sets, Cody will be lifting (19 + 2n) kilograms.

His partner, starts with 20 kilogram bar and increases this by 1 kilogram on each set.

In n sets, his partner will be lifting (20 + n) kilograms.

We are then asked to calculate when they will be lifting the same kilograms of weight.

When the amount of weight they are lifting becomes the same, we have,

19 + 2n = 20 + n

2n - n = 20 - 19

n = 1

So, in 1 set, they will be lifting the same weight.

when n = 1,

19 + 2n = 19 + 2(1) = 19 + 2 = 21 kilograms.

So, they will be lifting the same weight when they are both lifting 21 kilograms.

Hope this Helps!!!