Respuesta :
Question is Incomplete; Complete question is given below;
Cloud Nine is having a sale on all shirts and pants in the store. Olivia purchased 8 shirts and 4 pairs of pants for $176. Raheem purchased 3 shirts and 4 pairs of pants for $116. Let x represent the price of a shirt and y represent the price of a pair of pants. Write a system of equations, and use the elimination method to find a reasonable price for a pair of pants.
Answer:
The system of equations are [tex]\left \{ {{8x+4y=176} \atop {3x+4y=116}} \right.[/tex]
The reasonable price for pair of pants is $20.
Step-by-step explanation:
Let the price of shirt be 'x'.
Let price of pair of pants be 'y'.
Given:
Olivia purchased 8 shirts 4 pairs of pants for $176
So we can say that;
8 multiplied by the price of shirt plus 4 multiplied by the price of pair of pants is equal to 176.
framing in equation form we get;
[tex]8x+4y=176 \ \ \ \ equation \ 1[/tex]
Also Given:
Raheem purchased 3 shirts and 4 pairs of pants for 116.
So we can say that;
3 multiplied by the price of shirt plus 4 multiplied by the price of pair of pants is equal to 116.
framing in equation form we get;
[tex]3x+4y=116 \ \ \ \ equation \ 2[/tex]
Hence the system of equation are [tex]\left \{ {{8x+4y=176} \atop {3x+4y=116}} \right.[/tex]
Now by using elimination method we will subtract equation 2 from equation 1 we get;
[tex](8x+4y)-(3x+4y)=176-116\\\\8x+4y-3x-4y = 60\\\\5x =60\\\\x=\frac{60}{5}=\$12[/tex]
Now Substituting the value of x in equation 1 we get;
[tex]8x+4y=176\\\\8\times 12+4y =176\\\\96+4y=176\\\\4y =176-96\\\\4y = 80\\\\y= \frac{80}{4} =\$ 20[/tex]
Hence The reasonable price for pair of pants is $20.
