Question

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 ​170$ and first class tickets for ​970$. She used her total budget for airfare for the​ trip, which was ​4100$. How many first class tickets did she​ buy?

Answer 1

Sarah bought 3 first class tickets.

Step-by-step explanation:

To find the number of first class tickets Sarah bought, we can set up an equation based on the given information. Let x be the number of coach tickets and y be the number of first class tickets. We know that Sarah bought a total of 10 tickets, so x + y = 10. Additionally, we know that each coach ticket costs $170 and each first class ticket costs $970, and Sarah used her total budget of $4100. This can be represented by the equation 170x + 970y = 4100.

To solve this system of equations, we can use substitution or elimination. Let's solve it using elimination:

1. Multiply the first equation by 170 to make the coefficients of x the same: 170x + 170y = 1700.
2. Subtract the second equation from the first equation: (170x + 170y) - (170x + 970y) = 1700 - 4100.
3. Simplify the equation: -800y = -2400.
4. Divide both sides of the equation by -800: y = 3.

Therefore, Sarah bought 3 first class tickets.