Question

A magic show sold tickets for $2 for every child and $3 for every adult. The total sales were $118. The difference of two times the number of adults and half the children will total 20. Using the elimination method for the system of equations, what is the number of adults and children at the magic show?

Answer 1

3a + 2c = 118
2a - 0.5c = 20.....multiply by 4
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3a + 2c = 118
8a - 2c = 80 (result of multiplying by 4)
----------------add
11a = 198
a = 198/11
a = 18 <=== 18 adults

3a + 2c = 118
3(18) + 2c = 118
54 + 2c = 118
2c = 118 - 54
2c = 64
c = 64/2
c = 32.....32 children

Answer 2

9 adoults and 11 kids