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Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 10 people took the trip. She was able to purchase coach tickets for ​$260 and first class tickets for ​$1270. She used her total budget for airfare for the​ trip, which was ​$9670. How many first class tickets did she​ buy? How many coach tickets did she​ buy?

Respuesta :

Ashraf82

She bought 7 first class tickets

She bought 3 coach tickets

Step-by-step explanation:

Let us put the information of the problem in two equation and solve them

  1. The number of the people who took the trip including Sarah is 10
  2. The cost of each coach ticket is $260
  3. The cost of each first class tickets is $1270
  4. She used her total budget $9670 for airfare for the​ trip

We need to find the number of the coach tickets and first class tickets

she bought for the trip

Assume that the number of the coach tickets is x and the number of

the first class tickets is y

∵ Sara bought 10 tickets including her

∵ The number of the coach tickets = x

∵ The number of the first class tickets = y

∴ x + y = 10 ⇒ (1)

∵ The cost of the coach ticket = $260

∵ The cost of the first class ticket = $1270

∵ Her budget for the tickets = $9670

∴ 260x + 1270y = 9670 ⇒ (2)

Now let us solve the system of the equations to find x and y

Multiply equation (1) by -260 to eliminate x

∵ (-260)x + (-260)y = (-260)(10)

∴ -260x - 260y = -2600 ⇒ (3)

Add equations (2) and (3)

∴ 1010y = 7070

- Divide both sides by 1010

∴ y = 7

Substitute the value of y in equation (1) to find x

∵ x + 7 = 10

- Subtract 7 from both sides

∴ x = 3

She bought 7 first class tickets

She bought 3 coach tickets

Learn more:

You can learn more about solving the system of linear equations in

brainly.com/question/13168205

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