At a carnival, food tickets cost $2 each and ride tickets cost $3 each. A total of $1,240 was collected at the carnival. The number of food tickets sold was 10 less than twice the number of ride tickets sold.The system of equations represents x, the number of food tickets sold, and y, the number of ride tickets sold.2x + 3y = 1240 x = 2y – 10How many of each type of ticket were sold?
Answer
A
180 food tickets and 293 ride tickets
B
180 food tickets and 350 ride tickets
C
293 food tickets and 180 ride tickets
D
350 food tickets and 180 ride tickets
Explanation
Substitute x = 2y − 10 into the total-sales equation: 2(2y − 10) + 3y = 1,240. This gives 7y − 20 = 1,240, so y = 180 ride tickets. Then x = 2(180) − 10 = 350 food tickets, which is choice D: 350 food tickets and 180 ride tickets.
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