Question

Molly and Mary both go caroling over winter break. Molly has already stopped at 24 houses, and Mary has stopped at 8. Molly continues to carol at 3 houses per day, and Mary continues to carol at 7 houses per day. Write and solve an equation to show how many days it will be until they have caroled at the same number of houses. (Enter the number of houses for your answer.)

Answer 1

Molly and Mary will have caroled at the same number of houses, which is 36 houses, after 4 days.

Step-by-step explanation:

To find out how many days it will be until Molly and Mary have caroled at the same number of houses, we need to set up an equation where their respective houses caroled are equal. Molly starts with 24 houses and carols at 3 houses per day, so the number of houses she has caroled at after d days is 24 + 3d. Mary starts with 8 houses and carols at 7 houses per day, so her total is 8 + 7d after d days.

Setting the two expressions equal to each other, we have the equation:

24 + 3d = 8 + 7d

Solving for d, we subtract 3d from both sides:

24 = 8 + 4d

Then we subtract 8 from both sides:

16 = 4d

So, d equals 4 when we divide both sides by 4:

d = 4

Therefore, they will have caroled at the same number of houses after 4 days. To find the number of houses, we can plug d back into either equation:

Molly's houses: 24 + 3(4) = 24 + 12 = 36

Mary's houses: 8 + 7(4) = 8 + 28 = 36

So, they will have both caroled at 36 houses after 4 days.