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Two runners are saving money to attend a marathon.

- The first runner has [tex]$\$112$[/tex] in savings, received a [tex]$\$45$[/tex] gift from a friend, and will save [tex]$\$25$[/tex] each month.
- The second runner has [tex]$\$50$[/tex] in savings and will save [tex]$\$60$[/tex] each month.

Which equation can be used to find [tex]$m$[/tex], the number of months it will take for both accounts to have the same amount of money?

A. [tex]$112 - 25 m + 45 = 50 - 60 m$[/tex]
B. [tex]$112 + 25 + 45 m = 50 m + 60$[/tex]
C. [tex]$112 + 25 - 45 m = -50 m + 60$[/tex]
D. [tex]$112 + 25 m + 45 = 50 + 60 m$[/tex]

Answer :

Sure! Let's find the equation that can be used to determine the number of months [tex]\( m \)[/tex] it will take for both runners to have the same amount of money in their accounts. We'll approach solving this step by step.

### Step-by-Step Solution

1. First Runner's Savings Calculation:
- The first runner currently has \[tex]$112 in savings.
- They received a \$[/tex]45 gift from a friend.
- They save \[tex]$25 every month.

We can write an expression for the total amount of money the first runner will have after \( m \) months:
\[
\text{Total amount of first runner} = 112 + 45 + 25m
\]

2. Second Runner's Savings Calculation:
- The second runner currently has \$[/tex]50 in savings.
- They save \$60 every month.

We can write an expression for the total amount of money the second runner will have after [tex]\( m \)[/tex] months:
[tex]\[
\text{Total amount of second runner} = 50 + 60m
\][/tex]

3. Setting up the Equation:
To find the number of months [tex]\( m \)[/tex] when both runners will have the same amount of money, we set the two expressions equal to each other:
[tex]\[
112 + 45 + 25m = 50 + 60m
\][/tex]

4. Simplifying the Equation:
To simplify, we combine the constant terms on each side:
[tex]\[
112 + 45 = 157
\][/tex]
Therefore, the equation simplifies to:
[tex]\[
157 + 25m = 50 + 60m
\][/tex]

So, the correct equation that can be used to find [tex]\( m \)[/tex] is:
[tex]\[
112 + 25m + 45 = 50 + 60m
\][/tex]

This matches the option:
[tex]\[
\boxed{112 + 25m + 45 = 50 + 60m}
\][/tex]

I hope this helps! Let me know if you have any other questions.

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Rewritten by : Barada