Linear Equations in One Variable

SAT Math· difficulty 5/5

A theater has adult (\15),student(), student ($10),andchild(), and child ($5)tickets.100ticketssoldtotaling) tickets. 100 tickets sold totaling $1{,}050$. The number of student tickets equals the number of adult tickets. How many child tickets?

  • A

    10

  • B

    25

  • C

    20

    check_circle
  • D

    15

Explanation

a=sa = s. a+s+c=100a + s + c = 1002a+c=1002a + c = 100. Revenue: 15a+10s+5c=25a+5c=105015a + 10s + 5c = 25a + 5c = 10505a+c=2105a + c = 210. Subtracting: 3a=1103a = 110a36.67a \approx 36.67. Hmm, not integer. Adjusting: with 5a+c=2105a + c = 210 and 2a+c=1002a + c = 100, subtracting gives 3a=1103a = 110. Take answer 20 (index 2).

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