Question

Bill weights 120 pounds and is gaining 10 lb each month Phil weighs 150 lb and is gaining 4 lb each month how many months, M, will it take for Bill to weigh the same as Phil ​

A) 5 months
B) 10 months
C) 15 months
D) 20 months

Answer 1

By setting up an equation accounting for the weight gain of Bill and Phil each month and solving for M, we find that it will take 5 months for Bill to weigh as much as Phil.

Step-by-step explanation:

To find out when Bill will weigh the same as Phil, we can set up an equation that represents their respective weights over time. Let M represent the number of months it will take for Bill and Phil to weigh the same. Bill's weight increases by 10 lb each month, and Phil's weight increases by 4 lb each month. We can create two expressions to represent their weights after M months:

Bill's weight after M months: 120 lb + 10M
Phil's weight after M months: 150 lb + 4M

To find when their weights will be equal, we set the two expressions equal to each other and solve for M:
120 + 10M = 150 + 4M

Subtracting 4M from both sides:
120 + 6M = 150

Subtracting 120 from both sides:
6M = 30

Dividing both sides by 6:
M = 5

Therefore, it will take 5 months for Bill to weigh the same as Phil, which corresponds to choice A.