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?

John weighs 375 pounds, and Karen weighs 125 pounds.

Step-by-step 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: Karen's weight = 125 pounds

Step-by-step 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