Question

"Jimmy had bought 6 apples and 12 oranges for a total of $33. Emma had bought 20 apples and 15 oranges for the total of $60. Find the cost of one apple and one orange

Answer 1

we write the sentences in mathematical expressions

(x is the value for each apples and y for each oranges)

Jimmy had bought 6 apples and 12 oranges for a total of $33.

`6x+12y=33`

Emma had bought 20 apples and 15 oranges for the total of $60

`20x+15y=60`

now we try to solve the two equations

I will solve x from the first equation and replace on the second to find y

`\begin{gathered} 6x+12y=33 \\ 6x=33-12y \\ x=(33-12y)/(6) \end{gathered}`

replacing and solving y

`\begin{gathered} 20x+15y=60 \\ 20((33-12y)/(6))+15y=60 \\ 110-40y+15y=60 \\ -25y=60-110 \\ 25y=50 \\ y=2 \end{gathered}`

y=2 so, the cost of the orange is $2

now replace y=2 on any equation to find x

`\begin{gathered} 6x+12y=33 \\ 6x+12(2)=33 \\ 6x+24=33 \\ 6x=9 \\ x=1.50 \end{gathered}`

the cost of the apples is $1.50