Question

Help with 2 questions? giving you a medal!

A business has $15,000 to spend on airline tickets to travel to a conference. It wants 27 of its employees to attend. The business wants to buy as many business-class seats as possible. The business-class seats cost $700. The economy-class seats cost $375. How many of each type of ticket should the business purchase?

11 business class and 16 economy class

12 business class and 15 economy class

15 business class and 12 economy class

16 business class and 11 economy class


Given the equation 4x + 2y = 9, which equation below would cause an inconsistent-independent system?

6x + 12y = 13

2x + y = -6

x - 2y = 7

8x - 4y = -5

Answer 1

First Problem:
Assume the number of business class seats purchased to be x
There are 27 employees.
So what is the number of economy class seats purchased?

Answer 2

27 class seats ? :O

Answer 3

For 27 employees they need to buy 27 seats.
x of the seats are business class.
So the remaining seats has to be the economy class.
So you need to subtract x from 27.
Number of economy class seats = (27 - x)
Number of business class seats = x

One business class seat costs $700
How much would x business class seat cost?

Answer 4

i subtracted 700 from 27 and i got 673

Answer 5

No.
If one business class seat costs $700
Then x business class seats will cost 700x

One economy class seat costs $375
(27 - x) economy class seats will cost 375(27 - x)

Total cost is 700x + 375(27 - x) = 15000

Can you solve the above equation for x?

Answer 6

I think so, hold on

Answer 7

x=15?

Answer 8

Good!
So number of business class seats = x = 15.
Number of economy class seats = ?

Answer 9

can you write the equation for me to solve it ? the way i solved for x!

Answer 10

In one of my replies above it says Number of economy class seats = (27 - x)
You have solved for x.
So number of economy class seats = ?

Answer 11

economy class seats is 12? :o

Answer 12

Yes. Business class = 15 and Economy class = 12.

Answer 13

Thank you so much!! :)

Answer 14

Can you help me with question 2?

Answer 15

and can you help with this one too?
How many solutions will this system of equations have?

y = -3.5x - 3.5
y = -3.5x + 3.5

Answer 16

For question 2:

Start with the given equation 4x + 2y = 9
and divide each term by 2

Can you tell me what the equation will look like if each term is divided by 2?

Answer 17

OKay so i divided 4 to each side. 4x crossed out so now i have 2y over 4 equals 9 over 4. Where do i go from there?

Answer 18

No.
4x + 2y = 9
Take each term (that is 4x, 2y, 9) and divide it by 2 and tell me what the equation will look like?

Answer 19

If I divide each term by 2 the equation will be:
4x/2 + 2y/2 = 9/2
Can you simplify the above equation?

Answer 20

4x/2= 2? 2y/2=1? 9/2=4.5?
Am i on the right track?

Answer 21

It is:
2x + y = 4.5
Compare this equation to the 4 answers and tell me which one looks wrong.

Answer 22

x-2y=7 looks wrong

Answer 23

No.
The second answer says: 2x + y = -6

We are getting 2x + y = 4.5

The left hand sides are both the same. But the right hand sides are different. And that cannot happen. How can the same (2x + y) be -6 and also be 4.5?

So the second answer causes inconsistency and so the answer is the second choice.

Answer 24

Ohhhhh! thankyou so much, i understand it noww

Answer 25

The third problem has no solutions:
y = -3.5x - 3.5
y = -3.5x + 3.5