Select the correct answer.
Justin weighs 15 pounds less than Greg weighs. Half of Greg’s weight is 75 pounds less than Justin’s 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.
D. Greg weighs 170 pounds, and Justin weighs 155 pounds.
Let's solve this step-by-step:
Step 1: Justin weighs 15 pounds less than Greg weighs.
Let's assume Greg's weight as 'x'. So, Justin's weight would be 'x - 15'.
Step 2: Half of Greg’s weight is 75 pounds less than Justin’s weight.
Half of Greg's weight would be 'x/2'. According to the information given, this weight is 75 pounds less than Justin's weight.
So, we can write the equation as 'x/2 = (x - 15) - 75'.
Step 3: Solve the equation for 'x':
x/2 = x - 90
Multiply both sides of the equation by 2 to eliminate the fraction:
2(x/2) = 2(x - 90)
x = 2x - 180
180 = 2x - x
180 = x
So, Greg's weight is 180 pounds.
Step 4: Calculate Justin's weight:
Justin's weight is 15 pounds less than Greg's weight, so it would be 180 - 15 = 165 pounds.
Therefore, the answer is option C: Greg weighs 180 pounds, and Justin weighs 165 pounds.