M7MBA wrote: ↑

Sat Jun 12, 2021 5:31 am

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. \(22t + 23\)

Answer: A

Source: GMAT Prep

3 more $4 tickets than $7 tickets were purchased
Let 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 + 3

The question tells us that 2t + 1 tickets were purchased.
So, we can write: 2x + 3 = 2t + 1
Subtract 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 + 12
We'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 - 1

Take: 11x + 12
Substitute to get: 11(t - 1) + 12
Expand: 11t - 11 + 12
Simplify: 11t + 1

Answer: A

Cheers,
Brent