Question 660908

Hello, i have no idea on how to solve this problem :

Mr.santos gained 15%, based on cost, of selling 3/4 of a shipment of textiles. He sold the remainder at a lost of 10% of the cost. What percent of the cost did he gain on the entire shipment?

Please and thank you.


Let cost of textiles be C
Then ¾ of shipment cost ¾C, or {{{3C/4}}}
Since gain was 15% of ¾ of shipment, then he sold ¾ of shipment for {{{1.15(3C/4)}}}, or {{{3.45C/4}}}


Remainder of shipment = ¼, and cost ¼C, or {{{C/4}}}
Since loss was 10% of ¼ of shipment, then he sold the remaining ¼ for {{{.9(C/4)}}}, or {{{.9C/4}}}


Sale price of entire shipment = {{{3.45C/4 + .9C/4}}}, or {{{(3.45C + .9C)/4}}}, or {{{4.35C/4}}}


As cost of entire shipment = C, then gain on entire shipment = {{{4.35C/4 - C}}}, or {{{(4.35C - 4C)/4}}}, or {{{.35C/4}}}


Gain % on entire shipment = {{{(.35C/4)/C}}}, or {{{.35C/4C}}} ------ {{{.35cross(C)/4cross(C)}}} -----> {{{.35/4}}}, or {{{highlight_green(8.75)}}}%


If it's easier for you, you can use real numbers to arrive at the answer. When done, answer should be same as above.


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