Answer:rental cost for each movie = $3.5 rental cost for each video game = $5
Solution:
• Lets assume that rental cost for each movie = x
• and rental cost for each video game = y
Then ;
(1) Step 1 : write down an equation:
→8x + 3y = 43 .....( equation 1 )
→2x +5y = 32
∴ 5y = -2x + 32
y = (-2x +32 )/5.....(equation 2 )
(2) Substitude equation (2 ) into equation 1 :
→
[tex]\begin{gathered} 8x+\text{ 3 (}\frac{-2x+32}{5})\text{ = 43} \\ 8x\cdot\text{ 5 + 3(-2x+32) = 43 }\cdot5\text{ } \\ 40x\text{ -6x +96=215} \\ 34x\text{ = 215 -96 } \\ 34x\text{ = 119 } \\ x\text{ = }\frac{119}{34} \\ \therefore\text{ x = 3.5 } \\ \end{gathered}[/tex]This means that rental cost for each movie
(x) = $3.50 (3) Substitude x = $3.5 into equation 2 , then solve for y
y = (-2x +32 )/5
[tex]\begin{gathered} y\text{ = }\frac{-2x\text{ +32}}{5} \\ \text{ = }\frac{-2(3.5)+32\text{ }}{5} \\ \text{ =}\frac{-7\text{ +32}}{5} \\ \text{ =}\frac{25}{5} \\ \therefore\text{ y = 5 } \end{gathered}[/tex]This means that rental cost for each video game = $5.00
