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Mrs. Haworth sold 444 tickets to the rodeo. Student tickets cost $3 and adult tickets cost $5. Mrs. Haworth's sales totaled $1722. Is it reasonable that 220 adult tickets were sold? Justify your answer
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Let's check if it's reasonable to assume that 220 adult tickets were sold.
Let's use algebra to solve the problem. Let's denote the number of student tickets sold as 'S' and the number of adult tickets sold as 'A'.
We have two pieces of information:
Mrs. Haworth sold 444 tickets: S + A = 444
Total sales amounted to $1722: 3S + 5A = 1722
Now we can solve these two equations simultaneously to find the values of S and A.
Using the first equation, we can express S in terms of A: S = 444 - A.
Substituting this value of S into the second equation:
3(444 - A) + 5A = 1722
1332 - 3A + 5A = 1722
2A = 1722 - 1332
2A = 390
A = 195
So, according to the calculations, 195 adult tickets were sold. Since this is less than 220, it is not reasonable to assume that 220 adult tickets were sold.