## Algebra 1: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 6 - Systems of Equations and Inequalities - 6-2 Solving Systems Using Substitution - Practice and Problem-Solving Exercises - Page 375: 23

#### Answer

There were 9 adults and 2 children

#### Work Step by Step

Make two equations: x+y=11 and 22x+15y=228. X is the number of adults and y is the number of children. Isolate y in the first equation in order to be able to substitute it into the second equation: x+y=11 -subtract x from both sides- y=11-x Substitute the equation into the second equation: 22x+15y=228 -substitute- 22x+15(11-x)=228 -distribute- 22x+165-15x=228 -simplify like terms- 7x+165=228 -subtract 165 from both sides- 7x=63 -divide both sides by 7- x=9 Substitute x=9 into one of the equations to solve for Y: x+y=11 9+y=11 y=2 (9,2).There were 9 adults and 2 children

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