Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - 11.2 - 3 x 3 Systems of Equations - Problem Set 11.2: 25

Answer

The Helmet cost 250 dollars, the Jacket cost 350 dollars, and the Gloves cost 50 dollars.

Work Step by Step

Let g be the cost of the gloves, h be the cost of the helmet, and j be the cost of the jacket. Thus, we obtain: $ j + h + g = 650 \\ j = h + 100 \\ h + g = j -50$ In equation one, we plug in equation three to find: $ j + j -50 = 650 \\ 2j = 700 \\ j = 350$ We use equation two to find: $ h = j - 100 = 350 - 100 = 250 $ Since they add up in cost to 650 dollars, it follows: $ g = 650 - 350 - 250 = 50$
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