Bunuel wrote:
A person purchased a total of 2t + 1 tickets. Some of the tickets cost $4 each and the remaining tickets cost $7 each. If 3 more $4 tickets than $7 tickets were purchased, which of the following expresses the total cost, in dollars, of the 2t + 1 tickets?
A. 11t + 1
B. 11t + 12
C. 22t – 10
D. 22t + 11
E. 22t + 23
PS20417
These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach.
Enchanting has solved the question using the INPUT-OUTPUT approach, so let's solve it algebraically..
3 more $4 tickets than $7 tickets were purchasedLet x = the NUMBER of $7 tickets purchased
So, x + 4 = the NUMBER of $4 tickets purchased
So, the total NUMBER of tickets purchased = x + (x + 3) =
2x + 3The question tells us that
2t + 1 tickets were purchased.
So, we can write:
2x + 3 =
2t + 1Subtract 1 from both sides of the equation to get: 2x + 2 = 2t
Divide both sides by 2 to get: x + 1 = t
Subtract 1 from both sides to get:
x = t - 1 we'll use this information later on!Which of the following expresses the total COST, in dollars, of the 2t + 1 tickets?Let's first answer this question using the variables we assigned earlier.
The cost of x tickets costing $7 each = 7x dollars
The cost of x + 3 tickets costing $4 each = 4(x + 3) dollars
So, the TOTAL cost = 7x + 4(x + 3)
= 7x + 4x + 12
=
11x + 12We've now expressed the total cost in terms of x.
In order to express the total cost in terms of t, we'll use the fact that
x = t - 1Take:
11x + 12Substitute to get:
11(t - 1) + 12 Expand:
11t - 11 + 12 Simplify:
11t + 1Answer: A
Cheers,
Brent