Question

create a word problem for systems of equations.

School A and School B are selling tickets for their school play.Whoever sells the most tickets gets a mention in the local newspaper.School A sells 40 student tickets and 20 senior tickets for a total of $160.School B sold 10 student tickets and 60 senior tickets for a total of $100.

Answer 1

is this a good word problem to solve for graphing elimination and substituition.
@freckles @phi @Hero

Answer 2

@ganeshie8

Answer 3

not the way it is worded.

Answer 4

i dont understand what you mean what do i need to change

Answer 5

First, the question: who sells the most tickets does not use a "system of equations" to solve
you see school A sold 60 and B sold 70.

Second, system of equations (with 2 equations) should have two unknowns
I don't know what the unknowns are. Maybe price of each type of ticket, but unless both schools charge the same amount for each type (and we can't assume they do, unless you tell us), we are in trouble.

Answer 6

You can "tweak" the problem, by saying it's one school, and two people different people sold the tickets. (that way we know both used the same price for the "student ticket" and the "senior ticket"), and the problem is to figure out the price of each type of ticket.

Answer 7

sooo

Bridgette and ana are competing with each other to see who can sell the most tickets for their school play.Bridgette sold 20 senior tickets and 40 student tickets for a total of 110.Ana sold 40 senior tickets and 10 student tickets for a total of 100. find the cost of one senior ticket and one student ticket

Answer 8

is that better

Answer 9

yes, but now you have to solve the system to make sure the numbers make sense. You don't want the price to be negative (for example)

The easier way is to let the price be 1.00 and 2.00
then use those numbers to find:
20*1 + 40*2 = 20+80=100
so make the total dollars be 100
and for the other person
40*1 + 10*2= 40+20= 60 . so use 60 for the dollars the second person got.

Answer 10

or use your own prices (not mine)

Answer 11

so you want me to say that one total is 1.00 and the other total is 2.00

Answer 12

no, I am saying pick the "answers" (the prices) and use those numbers to figure out the total dollars (in your question)

Answer 13

if you pick the prices (I just gave an example using simple numbers like 1 and 2)
then you can figure out how much each person got.

Am I unclear?

Answer 14

im kinda confused so u want me to change the amount of tickets

Answer 15

If you make up a problem, you should know the answer to the problem (just in case you have to solve it, or check if someone else got the correct answer).

when you say
Bridgette sold 20 senior tickets and 40 student tickets for a total of 110.

how did you pick the 110 ?

Answer 16

Instead of randomly picking 110, I am saying "randomly pick the price of a senior ticket and the price of a student ticket" (those are the numbers someone would have to figure out)
then using your prices, you do
20*price of senior ticket + 40 * price of student ticket and get a number (not 110)
then use those same prices for the other person and get their total.

use those totals instead of the 110 and the 100 that you now are using.
that way, you know what the answer is (the prices you picked)

Answer 17

so im supposed to say
Bridgette sold 20 senior tickets and 40 student tickets

Answer 18

for a total of ****, and you need to put in some dollar amount.
I'm saying that you should not just pick 110, but instead, pick the prices and figure out how much the total comes to, using 20 senior and 40 student.

can you pick a price for a senior ticket and for a student ticket?

Answer 19

for a total of 2.00 bridgette sold 20 senior tickets and 40 student tickets.

Answer 20

you don't give the answer in the problem.
But you should pick the price for a senior ticket. what price do you want to use ?

Answer 21

6.00

Answer 22

bridgette is selling senior tickets for 6.00 and student tickets for 3.00 dollars

Answer 23

if bridgette sold 20 senior tickets at 6.00 per ticket, how many dollars did she get?

Answer 24

120

Answer 25

and she sold 40 student tickets at 3.00 per ticket. how much is that ?

Answer 26

120

Answer 27

and in total 120+120= 240

so use that number in your problem
Bridgette sold 20 senior tickets and 40 student tickets for a total of $240.00

now do the same for the other person. using 6 and 3, figure out how much their total is.

Answer 28

ana sold 10 senior tickets and 80 student tickets for a total of 240.00

Answer 29

10x6.00=60
80x3.00=240

Answer 30

yes, and 60+240 is 300

Answer 31

240+60=300

Answer 32

so ana sold her tickets for 300

Answer 33

so your statement should say
ana sold 10 senior tickets and 80 student tickets for a total of $300.00

Answer 34

now if someone solves your problem they should get back 6 and 3 for the prices

Answer 35

im supposed to solve my problem by using elimination substituition or graphing

Answer 36

the good news is you know the answers

Answer 37

Bridgette and ana are competing with each other to see who can sell the most tickets for their school play. Bridgette sold 20 senior tickets and 40 student tickets for a total of $240.00. Ana sold 10 senior tickets and 80 student tickets for a total of $300.00. Find the cost of one senior ticket and one student ticket.

Answer 38

to solve, first should give names to the two unknowns.
People usually use "x" and "y"
what should the x stand for ? (either price of senior tickets or the price of student tickets)

Answer 39

senior

Answer 40

so x+y=240.00

Answer 41

so you write:

x is the price of a senior ticket
y is the price of a student ticket

Answer 42

you should think about what you wrote. You *know* x is 6.00 and y is 3.00 (you picked them). so x+y is not going to be 240.00

but you are on the right track. How do we get 240 ?

Answer 43

20 * 6=120
40*3=120

Answer 44

yes. but we are not supposed to know the answer. instead of using the number 6 we use the "variable" x (which will be 6 after we figure it out)

in other words 20x is the total amount for the senior tickets (that means 20 times the (unknown) price)

Answer 45

20x+40y=240.00

Answer 46

exactly

Answer 47

and you need a 2nd equation (using Ana's info)

Answer 48

10x+80y=300.00

Answer 49

20x+40y=240.00
10x+80y=300.00

can you solve this ?

Answer 50

for elimination i could multiply 10 by -2 to eliminate the x's

Answer 51

yes, so multiply the entire equation (both sides and all terms) by -2

Answer 52

yea i know how to do the elimination process but how will i do the graphing how would i graph this

Answer 53

I would simplify both equations by multiplying them by 1/10
that gives us
2x+4y=24
x+8y= 30


then I would multiply the 1st equation by ½ so we have

x+2y=12
x+8y= 30

next, we plot these two lines.
there are a few ways. one way is write them in slope-intercept form

but all we need is 2 points, so I would pick x=0 and get 2y=12, y=6 or (0,6) is one point on the first line. then pick y=0, and we get x=12 so (12,0) is on the line.
plot those two points, and "connect the dots"

do the same thing for the other line.

or use geogebra or some on-line tool, and automatically plot them

Answer 54

thanks @phi