ANSWERS
• Equation:, s = 1000 + 55m
,
• Equation to save $10,000:, 10,000 = 1000 + 55m
,
• Months it takes you to save $10,000:, 164 months
EXPLANATION
You first deposit the $1000 your uncle gave you and then, each month, you add $55. So the first month the account will have,
[tex]1000+55[/tex]
After the second month, it will have,
[tex]1000+55+55[/tex]
And so on. Therefore, the equation that models your savings s after m months is,
[tex]s=1000+55m[/tex]
If we want to find how many months it will take to save $10,000 we have to solve the equation for s = 10,000:
[tex]10,000=1000+55m[/tex]
To solve it, subtract 1000 from both sides of the equation,
[tex]\begin{gathered} 10,000-1000=1000-1000+55m \\ 9000=55m \end{gathered}[/tex]
And divide both sides by 55,
[tex]\begin{gathered} \frac{9000}{55}=\frac{55m}{55} \\ 163.64\approx m \end{gathered}[/tex]
It will take at least 164 months to save $10,000.
