Question

You're going to the mall with your friendsand you have $200 to spend from yourrecent birthday money. You discover astore that has all jeans for $25 and alldresses for $50. You really, really want totake home 6 items of clothing because you"need" that many new things. How manypairs of jeans and how many dresses youcan buy so you use the whole $200 (taxnot included)?

Answer 1

Given that:

- You have $200 to spend.

- The store sells all jeans for $25 and all dresses for $50.

- You want to take home 6 items of clothing.

Let be "j" the number of jeans and "d" the number of dresses you can buy so you use the whole $200 (not including the tax).

Set up this System of Equations using the data provided in the exercise:

`\begin{cases}j+d=6{} \\ 25j+50d={200}\end{cases}`

You can follow these steps in order to solve the System of Equations using the Elimination Method:

1. You can multiply the first equation by -25:

`\begin{cases}-25j-25d={-150} \\ 25j+50d={200}\end{cases}`

2. Add the equations:

`\begin{gathered} \begin{cases}-25j-25d={-150} \\ 25j+50d={200}\end{cases} \\ ------------ \\ 0j+25d=50 \\ 25d=50 \end{gathered}`

3. Solve for "d":

`\begin{gathered} d=(50)/(25) \\ \\ d=2 \end{gathered}`

4. Substitute the value of "d" into the first original equation and solve for "j":

`\begin{gathered} j+(2)=6 \\ j=6-2 \\ j=4 \end{gathered}`

Hence, the answer is: You can buy 2 dresses and 4 jeans.