Question

three of Carlos and Clarita's friends are purchasing school supplies at the bookstore. Stan buys a notebook, three packages of pencils, and two markers for $7.50. Jan buys two notebooks, six packages of pencils, and five markers for $15.50. Fran buys a notebook, two packages of pencils, and two markers for $6.25. Based on the information in the instructions, write a system of equations to model the situation. Let n represent the price of a notebook, p represent the price of a package of pencils, and m represent the price of a marker. Your answer:How much does an individual notebook cost? Notebook: $ How much does a package of pencils cost? Pencil Package: $ How much does an individual marker cost? Marker: $

Answer 1

0. Building the equations for each friend.

We will use p to represent the pencils, m to represent the markers, and n to represent the notebooks.

• Stan

`n+3p+2m=7.50`

• Jan

`2n+6p+5m=15.50`

• Fran

`n+2p+2m=6.25`

To solve this system, we can do it by substitution: isolating the variable in one equation, replacing the expression in a second one, and doing the same until we have one equation with one variable.

2. Isolating n from Stan's equation:

`n=7.50-3p-2m`

3. Replacing this equation in Fran's equation and simplifying

`(7.50-3p-2m)+2p+2m=6.25`
`7.50-3p-2m+2p+2m=6.25`
`7.50-3p+2p=6.25`

As in this step, we have one equation with one letter, then we can get the value of p.

4. Getting the value of p

`3p-2p=7.50-6.25`
`p=1.25`

Now that we have the value of p we can use the isolated equation of n and the value of p in Jan's equation to solve for m.

5. Replacing the isolated expression of n and the value of p in Jan's equation and simplifying.

`2\cdot(7.50-3\cdot(1.25)-2m)+6\cdot(1.25)+5m=15.50`
`15-7.50-4m+7.50+5m=15.50`
`15+m=15.50`
`m=15.50-15`
`m=0.50`

6. Finally, we get n from the isolated expression.

`n=7.50-3\cdot(1.25)-2\cdot(0.5)`
`n=2.75`

Answer:

Based on the information obtained, we can say that...

• An individual notebook costs $2.75

,

• A package of pencils cost $1.25

,

• An individual marker costs $0.50