Quandaries and Queries

I have a hard time setting up equations in word problems and just cannot ever really understand them. I see the highest level of school that you mentioned is twelth grade and I am in my first year of college, but it is a problem that a high schooler would probably do, too.

My name is Christie and I am asking the question for myself so that I can understand this better.

Here is the word problem.

Sesame Street on Stage has different ticket prices for adults and for children under 6. Beth and her two children, ages 3 and 4, paid \$15 to gain entrance, while Jamie and John Jacobs and their 2-year old daughter got in for \$19.50. What is the ticket price for adults?

Christie Sharp

Hi Christie,

Think about having the tickets in your hand. For Beth you have 3 tickets, one adult and two children's tickets. The Jacobs also have three tickets, 2 adult and one child ticket. Suppose that the adult tickets cost \$A each and the children's tickets cost \$C each. You know what each family paid

 Beth \$A + \$C + \$C = \$15.00 The Jacobs \$A + \$A + \$C = \$19.50

These are the equations

A + 2C = 15.00

2A + C = 19.50

Subtracting the first equation from the second gives

A - C = 4.50

Thus an adult ticket costs \$4.50 more than a children's ticket.Thus if the Jacobs paid \$4.50 more they could have 3 adult tickets, and hence

3A = 19.50 + 4.50 = \$24.00

and hence

A = \$8.00

Penny

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