how many coach tickets and how many first class tickets

Question

INCLUDING SARAH A TOTAL OF 7 PEOPLE TOOK A TRIP .SHE PURCHASED COACH SEAT FOR 170.00 AND FIRST CLASS FOR 980.00 SHE HER TOTAL BUDGET FOR THE TRIP WHICH IS $2810. HOW MANY COACH TICKETS DID SHE BUY AND HOW MANY FIRST CLASS TICKETS DID SHE BUY

Answer 1

Let x be the number of first class and 7-x be the number of coach tickets.

980x +170(7-x) ≤ 2810

980x +1,190 -170x ≤  2810

810x  ≤ 1620

x ≤ 2

So either she bought  0, 1, or 2 first class tickets and 7, 6 or 5 coach tickets respectively.

0(980) + 7(170) < 2810 Less than her budget, but 1620 left over!

That's enough for 2 first class tickets!

1(980) + 6(170) > 2810 Too much for her budget! 

2(980) + 5(170) = 2810 Her budget exactly! 

She bought 5 coach tickets and 2 first class.

 

5(170) +2(980) = 2810

Answer 2

Let X equal the number of first class tickets purchased. Because there are 7 people going on the trip the number of coach tickets purchased must be (7-X). If we multiply the amount of each ticket by their respective price and add that amount together we get the total amount spent on tickets which must equal $2180. That equation looks like this:

 

$980*X + $170*(7-X) = $2810

 

$980X + $1190 - $170X = $2810

 

$810X = $1620

 

X = 2

 

Sarah purchased 2 First Class tickets and 5 Coach tickets.

Answer 3

So, Shafari, let's do this!

 

Let's let x = the number of coach seats and y = the number of first class seats.

 

There were 7 total seats, so x + y = 7

 

If she bought 2 coach seats, then she spent 170(2) = $340, right?

 

Buying x coach seats then costs 170x.  Buying y first class seats costs 980y.

 

Since the total was 2810, then 170x + 980y = 2810.

 

Now, let's take the first equation, x + y = 7, and solve it for either x or y.  Let's do x.

 

Subtracting y from both sides, we get x = 7 - y.  Yes, it's 1y, but we can't subtract it from 7 because 7 has no y.

 

Now, we take our "value" for x and substitute it for the x in the second equation.

 

170(7 - y) + 980y = 2810

 

Distributing, we get 1190 - 170y + 980y = 2810

 

We combine like terms to get 1190 + 810y = 2810

 

Subtracting 1190 from both sides, we get 810y = 1620

 

Dividing both sides by 810, we get y = 2.

 

Now, we can substitute this value for y into the first equation.

 

x + 2 = 7

 

Subtracting 2 from both sides, we get x = 5

 

So, Sarah bought 5 coach tickets and 2 first class tickets.

 

Hope this helps!