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A person purchased a total of 2t + 1 tickets. Some of the tickets cost

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A person purchased a total of 2t + 1 tickets. Some of the tickets cost  [#permalink]

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New post 22 May 2020, 10:29
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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



PS20417

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Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost  [#permalink]

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New post 23 May 2020, 11:35
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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 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

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Brent
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Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost  [#permalink]

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New post 22 May 2020, 10:47
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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


We will solve this by substitution.
    If t = 1, then number of tickets = 3
      Number of $ 4 tickets = 3
        Cost of $ 4 tickets = 12
      Number of $ 7 tickets = 0
        Cost of $ 7 tickets =0
      Total cost =12 = 11*1+1 = 11t+1
    We are getting 11t + 1 for any value of t.
Answer: Option A.
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Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost  [#permalink]

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New post 23 May 2020, 13:59
I took a lot of time to think on how to proceed with this question. Then thought why "+1", why not "2t" or just "t".

Then realized, 2t+1 is always odd and qtn also states that number of $4 tickets is 3 more than $7 tickets.

so tried t =1==> tickets = 3; it implies all $4 tickets; price = 12 i.e. 2t+1
t=2 ==> tickets = 5;tickets = 2 + 3; one each for $4 and $7 and 3 tickets extra for $4. Price = 1 tickets for $11 and 3 extra tickets for $12; total price = 23 i.e. (2t+1)
t=3 ==>tickets = 7; tickets = 4 + 3; two each for $4 and $7 and 3 tickets extra for $4. Price = 2 tickets for $11 and 3 extra tickets for $12 ; total price = 34 i.e. (2t+1)

I combined price of $4 and $7 = $11 and it means 2 tickets combined for $11 each ($4+$7)
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Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost  [#permalink]

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New post 25 May 2020, 12:12
Enchanting wrote:
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


We will solve this by substitution.
    If t = 1, then number of tickets = 3
      Number of $ 4 tickets = 3
        Cost of $ 4 tickets = 12
      Number of $ 7 tickets = 0
        Cost of $ 7 tickets =0
      Total cost =12 = 11*1+1 = 11t+1
    We are getting 11t + 1 for any value of t.
Answer: Option A.



Why did you considered all the 3 tickets as of 4$ and 0 for 7$?
I didn't get the highlighted part, can you elaborate please?
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Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost  [#permalink]

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New post 30 May 2020, 21:29

Solution



Given
In this question, we are given that
    • A person purchased a total of 2t + 1 tickets.
    • Some of the tickets cost $4 each and the remaining tickets cost $7 each

To find
We need to determine
    • 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

Approach and Working out
Let the number of $4 tickets be x, and the number of $7 tickets be y
    • x + y = 2t + 1
    • Cost = 4x + 7y

Now, if x = y + 3
    • Cost = 4(y + 3) + 7(y) = 11y + 12
    • And, 2y + 3 = 2t + 1
      o Implies, y = t - 1

    • Thus, Cost = 11(t – 1) + 12 = 11t + 1

Thus, option A is the correct answer.

Correct Answer: Option A
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Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost   [#permalink] 30 May 2020, 21:29

A person purchased a total of 2t + 1 tickets. Some of the tickets cost

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