Question

The school store is running a promotion on school supplies. Different supplies are placed on two shelves.• You can purchase 3 items from shelf A and 2 from shelf B for $26, or• You can purchase 2 items from shelf A and 5 from shelf 8 for $32.Let z represent the cost of an item from shelf A and let y represent the cost of an item from shelf B. Write and solve asystem of equations to find the cost of items from shelf A and shelf B. Show your work and thinking!

Answer 1

We define the following notation:

• z = cost of an item from shelf A,

,

• y = cost of an item from shelf B.

From the statement, we know that:

• 3 items from shelf A and 2 from shelf B cost $26, so we have:

`3z+2y=26,`

• 2 items from shelf A and 5 from shelf B for $32, so we have:

`2z+5y=32.`

We have the following system of equations:

`\begin{gathered} 3z+2y=26, \\ 2z+5y=32. \end{gathered}`

1) To solve this system, we multiply the first equation by 2 and the second equation by 3:

`\begin{gathered} 2\cdot(3z+2y)=2\cdot26\rightarrow6z+4y=52, \\ 3\cdot(2z+5y)=3\cdot32\rightarrow6z+15y=96. \end{gathered}`

2) We subtract equation 1 to equation 2, and then we solve for y:

`\begin{gathered} (6z+15y)-(6z+4y)=96-52, \\ 11y=44, \\ y=(44)/(11)=4. \end{gathered}`

We found that y = 4.

3) We replace the value y = 4 in the first equation, and then we solve for z:

`\begin{gathered} 3z+2\cdot4=26, \\ 3z+8=26, \\ 3z=26-8, \\ 3z=18, \\ z=(18)/(3)=6. \end{gathered}`

Answer

The cost of the items are:

• z = 6, for items from shelf A,

,

• y = 4, for items from shelf B.