Question

select the correct answer justin weighs 15 pounds less than greg weighs. half of gregs weight is 75 pounds less than justins weight. how much does each of them weigh? a. greg weighs 200 pounds, and justin weighs 185 pounds b. greg weighs 190 pounds, and justin weighs 175 pounds c. greg weighs 180 pounds, and justin weighs 165 pounds d. greg weighs 170 pounds, and justin weighs 155 pounds

Explanation:

Step1: Define variables

Let Greg's weight be \( G \) pounds and Justin's weight be \( J \) pounds.

Step2: Translate the first condition

Justin weighs 15 pounds less than Greg, so \( J = G - 15 \).

Step3: Translate the second condition

Half of Greg's weight is 75 pounds less than Justin's weight, so \( \frac{G}{2} = J - 75 \).

Step4: Substitute \( J \) from Step2 into Step3's equation

Substitute \( J = G - 15 \) into \( \frac{G}{2} = J - 75 \), we get \( \frac{G}{2} = (G - 15) - 75 \).

Step5: Simplify and solve for \( G \)

Simplify the right side: \( \frac{G}{2} = G - 90 \).
Multiply both sides by 2: \( G = 2G - 180 \).
Subtract \( G \) from both sides: \( 0 = G - 180 \), so \( G = 180 \).

Step6: Find \( J \) using \( J = G - 15 \)

Substitute \( G = 180 \) into \( J = G - 15 \), we get \( J = 180 - 15 = 165 \).

Answer:

C. Greg weighs 180 pounds, and Justin weighs 165 pounds.