Question

Demi and Juan start saving money for their vacation. Demi starts with $50 and saves $20 each week; Juan started with only $35, but saves $25 each week.a. Write expressions for Demi and Juan that represents the amount they saved in w weeks.b. If their vacation is in 4 weeks, who will have more money?Extension: Write the expression that represents their combined total. Write an expression that represents the difference the amount Juan and Demi have.

Answer 1

We need to write an expression for the savings of both Demi and Juan. For this we will call the number of weeks since they started saving "x".

Demi started with $50 and adds $20 every week, therefore her savings can be expressed by the following equation:

`\text{demi = 50+20}\cdot x`

Juan started with $35 and adds 25 each week, therefore his savings can be expressed by the following equation:

`\text{juan}=35+25\cdot x`

To calculate how much each will have in 4 weeks we need to apply the number 4 on the place of the variable x. We have:

`\begin{gathered} \text{demi = 50+20}\cdot4=50+80=130 \\ \text{juan}=35+25\cdot4=35+100=135 \end{gathered}`

Juan will have more money if their vacation is in 4 weeks.

To find the expression that represents their combined total we need to sum the expression for demi and juan. We have:

`\begin{gathered} \text{total}=\text{demi}+\text{juan} \\ \text{total}=50+20\cdot x+35+25\cdot x \\ \text{total}=85+45\cdot x \end{gathered}`