Question

The following image contains the problem I have please help

Answer 1

Answer:rental cost for each movie = $3.5 rental cost for each video game = $5

• 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 :

→

`\begin{gathered} 8x+\text{ 3 (}(-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{ = }(119)/(34) \\ \therefore\text{ x = 3.5 } \\ \end{gathered}`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

`\begin{gathered} y\text{ = }\frac{-2x\text{ +32}}{5} \\ \text{ = }\frac{-2(3.5)+32\text{ }}{5} \\ \text{ =}\frac{-7\text{ +32}}{5} \\ \text{ =}(25)/(5) \\ \therefore\text{ y = 5 } \end{gathered}`This means that rental cost for each video game = $5.00