Question

Question 8 set up and solve a set of equations to solve the problem

Answer 1

We have to set up and solve a system of equations.

We have to start by writing the equations to find the prices of the juice boxes and the BBQ sandwiches.

Let J be the price of a juice box and S the price of a BBQ sandwich.

If the Meyers purchased 4 juice boxes and 2 BBQ sandwiches for $16, we can write the total cost as the sum of the products of the number of units and the price of the juice boxes and the sandwiches:

`4\cdot J+2\cdot S=16`

In the same way, the Kaplinsky bought 4 juice boxes and 3 BBQ sandwiches for $21. Then, we can write:

`4\cdot J+3\cdot S=21`

Now we have two equations for two unknowns, J and S.

We can solve for S by substracting the first equation for the second one as:

`\begin{gathered} (4J+3S)-(4J+2S)=21-16 \\ 4J-4J+3S-2S=5 \\ 0J+1S=5 \\ S=5 \end{gathered}`

Knowing that a sandwich costs $5, we can calculate the cost of a juice box using any of the two equations:

`\begin{gathered} 4J+2S=16 \\ 4J+2\cdot5=16 \\ 4J+10=16 \\ 4J=16-10 \\ 4J=6 \\ J=(6)/(4) \\ J=1.5 \end{gathered}`

Now, we know the prices of both products.

If the Edwin family purchased 3 juice boxes and 3 BBQ sandwiches, we can calculate how much they spent as:

`\begin{gathered} C=3J+3S \\ C=3\cdot1.5+3\cdot5 \\ C=4.5+15 \\ C=19.5 \end{gathered}`

They spent $19.50.

Answer:

(1.5, 5)

Cost of a juice box = $1.50

Cost of a BBQ sandwich = $5

Money spent by Edwin family = $19.50