Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
EXPLANATION
Let's see the facts:
One month:
Rented movies = 5
Rented video games = 3
Total = $34
Next month:
Rented movies = 2
Rented video games = 12
Total = $73
Let's call x to the rental cost for each movie and y to the rental cost for each game, representing the given data on a system of equations give us the following expressions:
(1) 5x + 3y = 34
(2) 2x + 12y = 73
Now, we need to solve this system of equations:
Isolate x for 5x + 3y = 34:
[tex]\mathrm{Subtract\: }3y\mathrm{\: from\: both\: sides}[/tex][tex]5x+3y-3y=34-3y[/tex]Simplify:
[tex]5x=34-3y[/tex][tex]\mathrm{Divide\: both\: sides\: by\: }5[/tex][tex]\frac{5x}{5}=\frac{34}{5}-\frac{3y}{5}[/tex][tex]Simplify\colon[/tex][tex]x=\frac{34-3y}{5}[/tex][tex]\mathrm{Substitute\: }x=\frac{34-3y}{5}[/tex][tex]\begin{bmatrix}2\cdot\frac{34-3y}{5}+12y=73\end{bmatrix}[/tex][tex]Simplify\colon[/tex][tex]\begin{bmatrix}\frac{68+54y}{5}=73\end{bmatrix}[/tex][tex]\mathrm{Multiply\: both\: sides\: by\: }5[/tex][tex]\frac{5\left(68+54y\right)}{5}=73\cdot\: 5[/tex][tex]\text{Simplify:}[/tex][tex]68+54y=365[/tex][tex]\mathrm{Subtract\: }68\mathrm{\: from\: both\: sides}[/tex][tex]68+54y-68=365-68[/tex][tex]Simplify\colon[/tex][tex]54y=297[/tex][tex]\mathrm{Divide\: both\: sides\: by\: }54[/tex][tex]\frac{54y}{54}=\frac{297}{54}[/tex][tex]Simplify\colon[/tex][tex]y=\frac{11}{2}[/tex][tex]\mathrm{For\: }x=\frac{34-3y}{5}[/tex][tex]\mathrm{Substitute\: }y=\frac{11}{2}[/tex][tex]x=\frac{34-3\cdot\frac{11}{2}}{5}[/tex][tex]x=\frac{34-\frac{33}{2}}{5}[/tex][tex]x=\frac{\frac{35}{2}}{5}[/tex][tex]x=\frac{35}{2\cdot\:5}[/tex][tex]x=\frac{35}{10}[/tex][tex]\mathrm{Cancel\: the\: common\: factor\colon}\: 5[/tex][tex]x=\frac{7}{2}[/tex][tex]\mathrm{The\: solutions\: to\: the\: system\: of\: equations\: are\colon}[/tex][tex]x=\frac{7}{2},\: y=\frac{11}{2}[/tex]Now, as x=rental cost for each movie and y= rental cost for each video game, we can conclude:
Rental cost for each movie = $3.5
Rental cost for each video game = $5.5
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
