Question

1 1 point At a local market, 3 apples and 2 pears cost $2.70. Three apples cost the same as 4 pears. Type a system of equations to find the cost for one apple and the cost for one pear.

Answer 1

Let:

• a ,be the individual cost of an apple

,

• p , be the individual cost of a pear

" 3 apples and 2 pears cost $2.70" means:

`3a+2p=2.70`

And "Three apples cost the same as 4 pears" means:

`3a=4p`

Thereby, our system of equations would be:

`\mleft\{\begin{aligned}3a+2p=2.70 \\ 3a=4p\end{aligned}\mright.`

We can subsitute equation 2 in equation 1 and clear p, the cost of an individual pear, as following:

`\begin{gathered} 3a+2p=2.70 \\ \rightarrow4p+2p=2.70\rightarrow6p=2.70 \\ \rightarrow p=(2.70)/(6) \\ \rightarrow p=0.45 \end{gathered}`

Clearing a from equation 1:

`\begin{gathered} 3a=4p\rightarrow a=(4p)/(3) \\ \rightarrow a=(4(0.45))/(3) \\ \rightarrow a=0.60 \end{gathered}`

Therefore, an apple costs $0.60 and a pear costs $0.45