Beth and her cousin Albert both collect stamps. Beth currently has $80$ stamps in her collection, and she adds $4$ more each month. Right now, Albert only has $20$ stamps in his collection, but he adds $10$ more each month. $\newline$ Which equation can you use to find $m$ , the number of months it will take for Albert to have as many stamps as Beth? $\newline$ Choices: $\newline$ (A) $80 + 4m = 20 + 10m$ $\newline$ (B) $80 - 4m = 20 + 10m$ $\newline$ How many months will it take for Albert to have as many stamps as Beth? $\newline$ ____ months $\newline$

Full solution

Q. Beth and her cousin Albert both collect stamps. Beth currently has

80

stamps in her collection, and she adds

4

more each month. Right now, Albert only has

20

stamps in his collection, but he adds

10

more each month.

\newline

Which equation can you use to find

m

, the number of months it will take for Albert to have as many stamps as Beth?

\newline

Choices:

\newline

(A)

80 + 4m = 20 + 10m

\newline

(B)

80 - 4m = 20 + 10m

\newline

How many months will it take for Albert to have as many stamps as Beth?

\newline

____ months

\newline

Question Prompt: Question Prompt: Determine the number of months it will take for Albert to have as many stamps as Beth.
Step $1$ : Step $1$ : Set up the equation based on the information given. Beth starts with $80$ stamps and adds $4$ each month. Albert starts with $20$ stamps and adds $10$ each month. We need to find when they will have the same number of stamps.
Step $2$ : Step $2$ : Write the equation representing each person's stamp collection over time. For Beth: $80 + 4m$ , and for Albert: $20 + 10m$ . Set them equal to find when they have the same amount: $80 + 4m = 20 + 10m$ .
Step $3$ : Step $3$ : Solve for $m$ . Subtract $4m$ from both sides to get: $80 = 20 + 6m$ .
Step $4$ : Step $4$ : Subtract $20$ from both sides to isolate the term with $m$ : $60 = 6m$ .
Step $5$ : Step $5$ : Divide both sides by $6$ to solve for $m$ : $m = 10$ .