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:
[tex]3a+2p=2.70[/tex]And "Three apples cost the same as 4 pears" means:
[tex]3a=4p[/tex]Thereby, our system of equations would be:
[tex]\mleft\{\begin{aligned}3a+2p=2.70 \\ 3a=4p\end{aligned}\mright.[/tex]We can subsitute equation 2 in equation 1 and clear p, the cost of an individual pear, as following:
[tex]\begin{gathered} 3a+2p=2.70 \\ \rightarrow4p+2p=2.70\rightarrow6p=2.70 \\ \rightarrow p=\frac{2.70}{6} \\ \rightarrow p=0.45 \end{gathered}[/tex]Clearing a from equation 1:
[tex]\begin{gathered} 3a=4p\rightarrow a=\frac{4p}{3} \\ \rightarrow a=\frac{4(0.45)}{3} \\ \rightarrow a=0.60 \end{gathered}[/tex]Therefore, an apple costs $0.60 and a pear costs $0.45
