Help with word problem?

Question

Sarah took the advertising department from her company an a round trip to meet with a potential client. Including Sarah, 10 people took the trip. She was able to purchase coach tickets for $360, and first class tickets for $1020. She used her total airfare budget which was $8220. How many first class and coach tickets did she buy?

Answer 1

Halie Annistin,

 

budget is 8820 

 

Set up an equation:

 

X (360) + Y (1020) = 8820

 

The problem also gives you the total people = 10 people so you know that X + Y = 10  So you would assume that she would buy as many first class tickets as she can, then buy coach for the rest.  Without exhausting her budget she can only buy 7 first class, leaving 3 for coach:

 

so X = 3 and Y = 7

 

That will use 7140 + 1080 = 8220 of her budget.  So she will have 600 left in her budget, taking all 10 people.  

 

Hope this helps!

Answer 2

We can solve this by creating a system of equations and solving.

 

First, we know that 10 people were on the trip.  So, the number of coach tickets plus the number of first class tickets is equal to 10.  We can write this as c + f = 10.

 

Next, we know each coach ticket costs $360 and each first class tickets costs $1,020.  Sarah spent a total of $8,220.  That leads to the second equation:  $360 x number of coach tickets plus $1,020 x number of first class tickets is $8,220.

360c + 1020f = 8220. 

 

Solving the first equation for c, we get c = 10 - f.  We can then substitute 10 - f for c in the second equation to solve for f:

 

360 (10 - f) + 1020f = 8220

3600 - 360f + 1020f = 8220

660f = 4620

f = 7

 

Now that we know she bought 7 first class tickets, we can replace f with 7 in the first equation, solving for c:

 

c + 7 = 10

c = 3

 

Another tip - I always advise my students to use variables that will help them keep their information straight.  By using c for coach and f for first class, we avoid any confusion.