Sarah took the advertising department from her company on a round trip to meet with a potential client. A total of 9 people took the trip. She was able to purchase coach tickets for $380, and first class tickets for $1070. She used her total budget for airfare for the trip, which was $6180. How many first class tickets did she buy? How many coach tickets did she buy?
Let's assume Sarah bought x coach tickets and y first-class tickets.
The cost of a coach ticket is $380, so the total cost of coach tickets is 380x.
The cost of a first-class ticket is $1070, so the total cost of first-class tickets is 1070y.
According to the problem, she used her total budget of $6180 for airfare, so we can set up the equation:
380x + 1070y = 6180.
We also know that a total of 9 people took the trip, so the number of coach tickets plus the number of first-class tickets is equal to 9:
x + y = 9.
We can solve this system of equations to find the values of x and y.
Let's use the elimination method to solve these equations:
Since the first equation has a coefficient of 380 for x and the second equation has a coefficient of 1 for x, let's multiply the second equation by 380:
380x + 1070y = 6180,
380x + 380y = 3420.
By subtracting the second equation from the first equation, we can eliminate x:
(380x + 1070y) - (380x + 380y) = 6180 - 3420,
(1070y - 380y) = 2760,
690y = 2760.
Dividing both sides of the equation by 690 gives us:
y = 4.
Using this value of y, we can substitute it back into the second equation to find x:
x + 4 = 9,
x = 9 - 4,
x = 5.
Therefore, Sarah bought 5 coach tickets and 4 first-class tickets.
To determine the number of first class and coach tickets Sarah bought, we can set up a system of equations based on the given information.
Let's assume Sarah bought x first class tickets and y coach tickets.
According to the problem, a total of 9 people took the trip. Therefore, we can write:
x + y = 9 -- Equation 1
The cost of each first class ticket is $1070, and she bought x first class tickets. The cost of each coach ticket is $380, and she bought y coach tickets. She used her total budget of $6180 for airfare. So, we can write:
1070x + 380y = 6180 -- Equation 2
Now, we have a system of equations with two variables (x and y). We can solve this system to find the values of x and y.
Using Equation 1, we can express x in terms of y as follows:
x = 9 - y
Substituting this value of x into Equation 2, we get:
1070(9 - y) + 380y = 6180
9630 - 1070y + 380y = 6180
-690y = -3450
Dividing both sides of the equation by -690, we get:
y = 3450 / 690 = 5
Now, substituting the value of y back into Equation 1, we can find x:
x + 5 = 9
x = 9 - 5 = 4
Therefore, Sarah bought 4 first class tickets and 5 coach tickets.
3
4
first class --- x
coach ------- 9-x
1070x + 380(9-x) = 6180
solve for x
take it from there, (same type as your other post)