Question

24. Jenna wants to purchase a new guitar for $375. She currently has $45 in her savings account. If she plans to save $35 each week, how many weeks will it take her to save enough money to purchase the guitar?

Answer 1

We will determine how much time it takes for Jenna to buy a guitar.

First we will try to analyze Jenna's bak account situation. She has a certain amount of savings ( S ) and she plans to save ( r ) amount every week.

`\begin{gathered} S\text{ = \$45} \\ r\text{ = \$35} \end{gathered}`

We will express the amount that Jenna has in ( x ) number of weeks in her saving account:

`\begin{gathered} T\text{ = S + r}\cdot x \\ T\text{ = 45 + 35}\cdot x \end{gathered}`

Jenna wants to buy a guitar which costs ( c ) around:

`c\text{ = \$375}`

For her to buy a guitar which costs ( c ), she must have the same amount in her savings account ( T ). We will equate the two and solve for ( x ) to determine the minimum number of weeks required for her to save the cost of a guitar:

`\begin{gathered} T\text{ = c} \\ 45\text{ + 35}\cdot x\text{ = 375} \end{gathered}`

We have a single variable equation which can be solved by algebraic manipulation as follows:

`\begin{gathered} 35\cdot x\text{ = 330} \\ \\ x\text{ = }(330)/(35) \\ \\ x\text{ = }9.43\text{ w}eeks\text{ }\approx\text{ 10 w}eeks \end{gathered}`

Therefore, she