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A person purchased a total of 2t + 1 tickets. Some of the ti
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09 Jul 2020, 11:28
09 Jul 2020, 11:28
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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
A. 11t + 1
B. 11t + 12
C. 22t – 10
D. 22t + 11
E. 22t + 23
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Re: A person purchased a total of 2t + 1 tickets. Some of the ti
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10 Jul 2020, 07:28
10 Jul 2020, 07:28
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Carcass 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
A. 11t + 1
B. 11t + 12
C. 22t – 10
D. 22t + 11
E. 22t + 23
These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach.
Let's solve it algebraically..
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
gmatclubot
Re: A person purchased a total of 2t + 1 tickets. Some of the ti [#permalink]
10 Jul 2020, 07:28
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