Question

John weighs three times as much as Karen. Two times John’s weight plus Karen’s weight is 875 pounds. How much does John weigh? How much does Karen weigh?

Answer 1

John weighs 375 pounds, and Karen weighs 125 pounds.

Explanation:

The best way to solve this question is to assign the weights to variables.

Let's give variable j to John's weight and k to Karen's.

If John weighs 3 times as much as Karen, j=3k.

If 2x John's weight plus 1x Karen's weight = 875, then 2j + k = 875,

which can also be written as 6k + k = 875 since we established that j=3k and 2*3=6.

Now all we need to do to find k is solve the equation:

6k + k = 875 combine common factors

7k = 875 divide both sides by 7

k = 875/7

k = 125

Now that we know Karen's weight, we can find John's weight by using j=3k.

Plug the now known value of k in:

j=3k

j=3(125)

j=375

Now you have your pair:

j=375, k = 125.

Answer 2

Answer: Karen's weight = 125 pounds

Explanation:

Let Karen's weight be x , this means that John's weight is 3x.

Two times John’s weight = 2(3x)

Two times John’s weight plus Karen’s weight is 875 pounds implies;

2(3x) + x = 875

6x + x = 875

7x = 875

divide through by 7

x = 125

Therefore Karen's weight = 125 pounds

John's weight = 3 x 125 = 375 pounds