Question

The cost of 8 boxes of paper clips and 7 boxes of staples cost $44.95. 5 boxes of paper clips and 3 boxes of staples cost $22.8. What is the cost of each box of paper clips and each box of staples

Answer 1

Cost of each box of paper clips is $2.25 and cost of each box of staples $3.85

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;

`8x+7y = 44.95 \ \ \ \ equation\ 1`

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;

`5x+3y = 22.8 \ \ \ \ equation\ 2`

Now Multiplying equation 2 by 7 we get;

`7(5x+3y)=22.8*7\\\\35x+21y = 159.6 \ \ \ \ equation \ 3`

Now Multiplying equation 1 by 3 we get;

`3(8x+7y) = 44.95* 3\\\\24x+21y = 134.85 \ \ \ \ equation \ 4`

Now Subtracting equation 4 from equation 3 we get;

`(35x+21y)- (24x+21y)= 159.6-134.85\\\\35x+21y-24x-21y = 24.75\\\\11x = 24.75\\\\x= (24.75)/(11) = \$2.25`

Now Substituting the value of x in equation 1 we get;

`8x+7y=44.95\\\\8* 2.25+7y =44.95\\\\18 + 7y = 44.95\\\\7y= 44.95-18\\\\7y = 26.95\\\\y=(26.95)/(7)= \$3.85`

Hence Cost of each box of paper clips is $2.25 and cost of each box of staples $3.85