Question

Regina, Phil, and Joseph each wrote expressions to represent their monthly weight, where m represents the number of months.

Regina: 10m + 120
Phil: 4m + 150
Joseph: 2(2m + 75)

How many months will it take for Regina and Joseph to weigh the same amount?
A. 5 months
B. 10 months
C. 15 months
D. 20 months

Answer 1

By setting the expressions for Regina and Joseph equal to each other and solving for m, we find that it will take 5 months for their weights to be equal.

Step-by-step explanation:

To determine how many months it will take for Regina and Joseph to weigh the same amount, we need to set their expressions equal to each other and solve for m. Regina's expression is 10m + 120 and Joseph's expression, when simplified, is 2(2m + 75) which equals 4m + 150.

We set up the equation: 10m + 120 = 4m + 150.
Subtracting 4m from both sides gives us:
6m + 120 = 150.
Subtracting 120 from both sides we have:
6m = 30.
Dividing both sides by 6 we get:
m = 5.

Therefore, it will take 5 months for Regina and Joseph to weigh the same amount.