Respuesta :
Answer:
Cost of each box of paper clips is $2.25 and cost of each box of staples $3.85
Step-by-step explanation:
Let the cost of 1 box of paper clips be 'x'.
Let the cost of 1 box of stapler be 'y'.
Given:
The cost of 8 boxes of paper clips and 7 boxes of staples cost $44.95.
So framing the above quote in equation form we get;
[tex]8x+7y = 44.95 \ \ \ \ equation\ 1[/tex]
Also Given:
The cost of 5 boxes of paper clips and 3 boxes of staples cost $22.8.
So framing the above quote in equation form we get;
[tex]5x+3y = 22.8 \ \ \ \ equation\ 2[/tex]
Now Multiplying equation 2 by 7 we get;
[tex]7(5x+3y)=22.8\times7\\\\35x+21y = 159.6 \ \ \ \ equation \ 3[/tex]
Now Multiplying equation 1 by 3 we get;
[tex]3(8x+7y) = 44.95\times 3\\\\24x+21y = 134.85 \ \ \ \ equation \ 4[/tex]
Now Subtracting equation 4 from equation 3 we get;
[tex](35x+21y)- (24x+21y)= 159.6-134.85\\\\35x+21y-24x-21y = 24.75\\\\11x = 24.75\\\\x= \frac{24.75}{11} = \$2.25[/tex]
Now Substituting the value of x in equation 1 we get;
[tex]8x+7y=44.95\\\\8\times 2.25+7y =44.95\\\\18 + 7y = 44.95\\\\7y= 44.95-18\\\\7y = 26.95\\\\y=\frac{26.95}{7}= \$3.85[/tex]
Hence Cost of each box of paper clips is $2.25 and cost of each box of staples $3.85
