SOLUTION: Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $2.00 each and Kathy selling adult tickets for $5.50 each. If their total income fo

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Question 244865: Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $2.00 each and Kathy selling adult tickets for $5.50 each. If their total income for 30 tickets was $105.50, how many did Ron sell ANSWER CHOICES: a. 18 tickets b. 13 tickets c. 19 tickets d. 17 tickets
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
a = number of tickets that ron sold.
b = number of tickets that kathy sold.

total number of tickets they sold is 30.

formula for that is:

a + b = 30

ron sells tickets at 2 dollars apiece.
kathy sells tickets at 5.50 apiece.

total income is 105.5

formula for that is:

2*a + 5.5*b = 105.5

two equations need to be solved simultaneously.

they are:

a + b = 30

2*a + 5.5*b = 105.5

use substitution.

take first equation and solve for a.

you get a = 30 - b

substitute for a in second equation to get:

2*a + 5.5*b = 105.5 becomes:

2 * (30-b) + 5.5*b = 105.5

simplfy to get:

60 - 2*b + 5.5*b = 105.5

combine like terms to get:

60 + 3.5*b = 105.5

subtract 60 from both sides to get:

3.5*b = 105.5 - 60 = 45.5

divide both sides by 3.5 to get:

b = 13

since a + b = 30, this means that:

a = 17
b = 13

sum = 30

a is equal to the number of tickets that ron sold which means that your answer is 17.

that would be selection d.

confirm your answer by substituting in original equations.

17 + 13 = 30 is confirmed.

2*17 + 5.5*13 = 34 + 71.5 = 105.5 is confirmed.