Question

Three hamburgers and 2 hotdogs cost $16 and 2hamburgers and 3 hotdogs cost $14. What is the costof one hamburger and one hotdog?

Answer 1

The cost of one hamburger is $4

The cost of one hotdog is $2

Step-by-step explanation

Let a represents hamburger, and

Let b represents hotdog.

Three hamburgers and 2 hotdogs cost $16 implies;

`3a+2b=16---i`

Also, 2 hamburgers and 3 hotdogs cost $14 implies;

`2a+3b=14---ii`

Compare the system of equations and solve using elimination method

`\begin{gathered} 3a+2b=16---i\text{ x 3} \\ 2a+3b=14---ii\text{ x 2} \\ \Rightarrow9a+6b=48---iii \\ 4a+6b=28---iv \\ \end{gathered}`

Substract (iv) from (iii)

`\begin{gathered} 9a-4a+6b-6b=48-28 \\ 5a=20 \\ D\text{ivide both sides by 5} \\ (5a)/(5)=(20)/(5) \\ a=4 \end{gathered}`

Since a represent hamburger, this implies the cost of one hamburger is $4

To get the cost of one hotdog, substitute a = 4 into (i)

`\begin{gathered} \text{Recall (i);} \\ 3a+2b=16---i \\ \Rightarrow3(4)+2b=16 \\ 12+2b=16 \\ 2b=16-12 \\ 2b=4 \\ \text{Divide both sides by 2} \\ (2b)/(2)=(4)/(2) \\ b=2 \end{gathered}`

Therefore, the cost of one hotdog is $2