Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 6 - Systems of Equations and Inequalities - 6-2 Solving Systems Using Substitution - Lesson Check - Page 371: 5


7 singing acts 5 comedy acts

Work Step by Step

Let s be the number of singing acts, and let c be the number of comedy acts. The show has 12 acts, so: $s+c=12$ The show lasts 50 minutes. Using the lengths given for each show: $5s+3c=50$ Step 1: Solve for s in the first equation. $s+c=12$ $s+c-c=12-c$ $s=12-c$ Step 2: Substitute "$12-c$" for s in the second equation and solve for c. $5s+3c=50$ $5(12-c)+3c=50$ $60-5c+3c=50$ $60-2c-60=50-60$ $-2c=-10$ $-2c\div-2=-10\div-2$ $c=5$ Step 3: Substitute 5 for c in the first equation and solve for s. $s+c=12$ $s+5=12$ $s+5-5=12-5$ $s=7$ Substitute the values into each equation to check the answer. $s+c=12$ $7+5=12\checkmark$ $5s+3c=50$ $5(7)+3(5)=50$ $35+15=50$ $50=50\checkmark$
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