MAT101 MOD2 - SLP

# MAT101 MOD2 - SLP - Let the cost of the first car part be x...

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RODNEY BUCKMIRE MAT101 – Module 2 – SLP Dr. Schek Part I: We had a party where we consumed a total of 10 bags of chips. We had x bags of Doritos and y bags of BBQ. BBQ costs \$1.00 per bag, Doritos costs \$2.00 If we spent \$17.00 on bags of chips, how many bags of Doritos did we have? x + y = 10 2.00x + 1.00 y = 17 then x = 3 and y = 7 So we had 3 bags of Doritos and 7 bags of BBQ. PART II: Let’s say my father sold two car parts for \$1520 thereby making a profit 25% on the first part and 10% profit on the other, whereas had he approached any retailer he would have sold them together for \$1535 with a profit of 10% on the first and 25% on the other car part. He has asked you to find out and tell him what the actual cost of each car part was.
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Unformatted text preview: Let the cost of the first car part be x and that of the second be y. Selling price of the first = cost price + profit = x + 0.25x = 1.25x Selling price of the second = cost price + profit = y + 0.10y = 1.10y Total revenue = 1.25x + 1.10y = 1520 ⇒ y = (1520 – 1.25x)/1.10 --- (1) Similarly in the retailer case, 1.10x + 1.25y = 1535 --- (2) Plug this in place of y in (2) then we get 1.10x + 1.25[(1520 – 1.25x)/1.10] = 1535 1.10x + 1727.27 – 1.42x = 1535 On solving we get x = \$600 and y = [1520 – 1.25 × 600]/1.10 = \$700. Solution: (x, y) = (\$600, \$700) The costs of the two car parts were \$500 and \$700 This system is consistent and independent. It has a unique solution....
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