Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 9 - Systems and Matrices - Test - Page 957: 9

Answer

The units ordered from suppliers in Toronto, Montreal, and Ottawa are $22,56,22$ respectively.

Work Step by Step

1. Assume the units ordered from suppliers in Toronto, Montreal, and Ottawa are $x,y,z$ 2. Based on the given conditions, we have: $\begin{cases} x+y+z=100 \\ 80x+50y+65z=5990 \\ x=z \end{cases}$ 3. Use the third equation in the other two, we have $\begin{cases} 2x+y=100 \\ 145x+50y=5990 \end{cases}$ 4. Multiply -50 to the first equation to get $-100x-50y=-5000$, then add it to the second equation, we have $45x=990$, thus $x=22$ 5. We have $y=100-2x=56$ and $z=x=22$ 6. The units ordered from suppliers in Toronto, Montreal, and Ottawa are $22,56,22$ respectively.
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