## Elementary Algebra

Published by Cengage Learning

# Chapter 11 - Additional Topics - 11.2 - 3 x 3 Systems of Equations - Problem Set 11.2 - Page 484: 22

#### Answer

She has 15 ones, 3 fives, and 6 twenty dollar bills.

#### Work Step by Step

Let o be the number of ones, f be the number of fives, and t be the number of twenty dollar bills. Thus, we obtain: $o + t + f = 24 \\ o + 20t + 5f = 150 \\ t = 2f$ We know from equation one that $o = 24 - t -f.$ We plug this into equation two to find: $24 + 19t + 4f = 150$ We plug in equation three to find: $38f + 4f = 126 \\ 42f = 126 \\ f =3$ Thus, we find: $t = 2f = 2(3) = 6$ Since there are 24 bills, we find: $o = 24 - 6 -3 = 15$

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