Question

Lola paid $13 for 6 greeting cards. Some cost $2 each, and some cost $3 each. Write and solve a system of equations to represent this situation. Interpret the solution

Answer 1

Step-by-step explanation

Let the number of each type of greeting cards be represented by x and y.

Since there are 6 greeting cards in total; it follows that:

`x+y=6----i`

If x greeting card costs $2 each, then the total cost of that type of card = 2x

Also, if y greeting card costs $3 each, then the total cost of that type of card = 3y.

Therefore, if Lola paid $13 for the 6 greeting cards, it follows that:

`2x+3y=13----ii`

Hence, the system of equations that represent this situation is:

`\begin{gathered} x+y=6-----i \\ 2x+3y=13---ii \end{gathered}`

To solve the system of equations, use the elimination method.

Multiply (i) by 3

`\begin{gathered} x+y=6----i*3 \\ 3x+3y=18---iii \\ \text{Substact (}ii)\text{ from (}iii) \\ 3x-2x+3y-3y=18-13_{} \\ x=5 \end{gathered}`

To solve for y, put x = 5 into equation (i)

`\begin{gathered} \text{Recall (i)} \\ x+y=6----i \\ 5+y=6 \\ y=6-5 \\ y=1 \end{gathered}`

Hence, the solution to the system of equations is x = 5, and y = 1

The interpretation of the solution

x = 5 implies there are 5 greeting cards that cost $2 each.

y = 1 implies there is 1 greeting card that cost $3 each.