Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Two friends visited a taffy shop. Vicky bought 4 kilograms of strawberry taffy and 3 kilograms of banana taffy for $28. Next, Edna bought 1 kilogram of strawberry taffy and 2 kilograms of banana taffy for $12. How much does the candy cost?

Answer 1

strawberry taffy costs $4 each and banana taffy costs $4 each

Step-by-step explanation:

We have the following information:

Two friends visited a taffy shop

Vicky bought 4 kilograms of strawberry taffy and 3 kilograms of banana taffy for $28.

Edna bought 1 kilogram of strawberry taffy and 2 kilograms of banana taffy for $12

Let the strawberry taffy be represented by ''x'' & banana taffy be represented as ''y''

The system of equations below is generated:

`\begin{gathered} 4x+3y=28-------1 \\ x+2y=12-------2 \\ \text{Using the Elimination Method, let's multiply }equation\text{ 2 by ''4'', we have:} \\ 4\cdot x+4\cdot2y=4*12 \\ 4x+8y=48-----3 \\ \text{Subtract equation 1 from equation 3, we have:} \\ 4x-4x+8y-3y=48-28 \\ 5y=20 \\ \text{Divide both sides by ''5'', we have:} \\ y=(20)/(5) \\ y=4 \\ \text{Substitute ''y'' into equation 2, we have:} \\ x+2y=12 \\ x+2(4)=12 \\ x+8=12 \\ \text{Subtract ''8'' from both sides, we have:} \\ x=12-8 \\ x=4 \\ \\ \therefore x=4,y=4 \end{gathered}`

Therefore, strawberry taffy costs $4 each, and banana taffy costs $4 each