[email protected] wrote:A certain charity sold tickets for its annual ball. If $5 of every ticket sold was donated to a children's center, what was the total amount of money donated to the children's center?
1.The total revenue from ticket sales was $1400.
2.If the charity had sold 30 more tickets, the amount of money donated to the children's center would have increased by 30 percent.
Target question:
What was the total amount of money donated to the children's center?
Given: $5 of every ticket sold was donated to a children's center
If we let
T = total number of tickets sold, then the total amount of money donated to the children's center = 5T. This allows us to rephrase the target question as follows...
Rephrased target question:
What is the value of 5T?
Statement 1: The total revenue from ticket sales was $1400
In order to determine the value of T, we need to know the ticket price. Otherwise, we have several conflicting possibilities. Here are two of them.
Case a: tickets are $1400 each, in which case T = 1, which means
5T = 5
Case b: tickets are $100 each, in which case T = 14, which means
5T = 70
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: If the charity had sold 30 more tickets, the amount of money donated to the children's center would have increased by 30 percent.
Start with a word equation:
($ donated if 30 more tickets were sold) = 130% of ($ actually donated)
In other words ($ donated if T + 30 tickets were sold) = 130% of ($ donated when T tickets are sold)
In algebraic terms, 5(T + 30) = 1.30(5T)
IMPORTANT: At this point, we should recognize that we
could solve this equation for T, in which case we could
definitely find the value of 5T
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
