Question

HELP! bowling costs $2.00 a game and video games cost $.50 each. Ron bowls x games, plays y video games, and spends $22.50. Ed bowls y games, plays x video games, and spends $15.00. Write a system of equations that can be used to find how much of each game they play.

Answer 1

@zepdrix sorry for bothering you soo much but can you help me again? :c

Answer 2

so first construct two equations that relate to each other based on the information you have been given

Answer 3

can you do that?

Answer 4

no i need help please

Answer 5

so you cant come up with at least one equation? Hint, the second sentence gives you one of your equations

Answer 6

x+y= 22.50

Answer 7

right :)

Answer 8

how do i do the 2nd one?

Answer 9

now the third sentence gives you the other one

Answer 10

y+x= 15.00

Answer 11

but what about the other numbers? 2.00 and .50?

Answer 12

well your equations are wrong actually but they are close, now remember that x number of bowling games costs 2dollars
and y number of video games cost 0.5 dollars

Answer 13

Hint you need to use multiplication

Answer 14

i need help ???

Answer 15

well your equations aren't exactly wrong but, if we were to apply systems of equations to them you would get the wrong answer because you are not accounting for the cost of x or the cost of y in the equation

Answer 16

ok can you tell me the equations please ?

Answer 17

if a soda costs 5 dollars and I spent 10 dollars on x number of sodas, how many sodas would I have?

can you solve that?

Answer 18

but i need an equation for my problem

Answer 19

I know, I'm trying to help you :) I'm not just messing with you relax this problem relates directly to your problem I pormise

Answer 20

promise*

Answer 21

Can you set up an equation for the problem I just gave you?

Answer 22

i dont know how to solve it :c im not very good at it

Answer 23

5x=10 ?

Answer 24

just think about it, If I spend 10 dollars on 5 dollars sodas how many would I have bought?

Answer 25

2

Answer 26

right can you write an expression for that? where x = the number of sodas I purchased

Answer 27

i dont know :C

Answer 28

hint use multiplication

Answer 29

i really dont know :( :(

Answer 30

The expression would be
5x = 10

do you understand why?

Answer 31

wait i said that above and you didnt say anything

Answer 32

lol sorry I missed that I'm making food sorry

Answer 33

Now apply that to the equations you just made, they work the same only you have two different items

Answer 34

lol its ok but can you please please help me with my problem?

Answer 35

i dont know how to start

Answer 36

Well if I bought two sodas one was worth 2 dollars and another was worth 3 dollars and I spent 10 dollars, could you write an expression for that?

Answer 37

2x+ 3y= 10

Answer 38

:)

Answer 39

hooray

Answer 40

now do the same thing with your question

Answer 41

but i dont get how to do it in my problem

Answer 42

theres so many numbers

Answer 43

because it is exactly the same only with video games and bowling instead of sodas

Answer 44

well you have two different equations

Answer 45

2x+0.50y= 22.50

Answer 46

2x+0.50y=15 ?

Answer 47

right, now the second one

Answer 48

idk theres 2 different pepple with different amounts

Answer 49

yeah perfect :)

Answer 50

thats the 2 equations?

Answer 51

now for the fun part, the algebra do you understand how systems of equations work?

Answer 52

yup, elimination or subsitution

Answer 53

yeah that is you are right? Do you have a better understanding why it is right now though?

Answer 54

well what you are doing really is finding where both these equations are equal

Answer 55

wait how would you solve these equations

Answer 56

equal to the same thing, their intersection(s)

Answer 57

im confused

Answer 58

but then they would both cancel out

Answer 59

thats not right??

Answer 60

System of equations is easy

solve for one of the variables in one of your equations

Answer 61

can you do that?

Answer 62

yes

Answer 63

ok show me what you get

Answer 64

y= 45+4x

Answer 65

i solved for y in the 1st equation :(

Answer 66

idk please help me

Answer 67

????

Answer 68

are you there?

Answer 69

Your two equations being:
2x+0.50y= 22.50
2x+0.50y=15

so first pick an equation and solve for one of the variables
so I will pick 2x+0.50y= 22.50
now I will solve for x (it doesnt matter which variable you choose just choose the one easiest to isolate)

2x + 0.50y = 22.50
2x = 22.50 - 0.50y
x = (22.50 - 0.50y)/2
x = 22.50/2 - 0.5y/2


Now it is simple as subing x into the other equation 2x+0.50y=15

so

2x+0.50y=15
becomes
2(22.50/2 - 0.5y/2) + 0.50y = 15

now you just need to solve for y

once you find y you can plug that into one of your original equations and solve for x

Answer 70

yeah you are right they will cancel out ugh my brain, sorry exam time

Answer 71

then the equations are wrong?? :(

Answer 72

since both lines are parallel, wow I feel dumb.

https://www.wolframalpha.com/input/?i=graph+2x%2B0.50y%3D+22.50%2C+2x%2B0.50y%3D15

If you look the graphs of both of these equations you will see that they never intersect

Answer 73

yeah

Answer 74

can you help me?

Answer 75

what systems of equations does is tells you where the two equations intersect. No the equations are correct

Answer 76

i dont know

Answer 77

??????????

Answer 78

are you there???

Answer 79

oh I just figured out the other equation

15.00 + 22.50 = 37.5 dollars total spent

$37.5 = 2x + 0.5y

this tells how many games in total have been played with the money spent, thus we can just use one of the two equations to figure out the amount they played each thing

Answer 80

nvm https://www.wolframalpha.com/input/?i=graph+2x%2B0.50y%3D+22.50%2C+2x%2B0.50y%3D15%2C+37.5+%3D+2x+%2B+0.5y

Answer 81

this is a trick question, you cant even solve this problem

Answer 82

yes you can theres a way idk it

Answer 83

You aren't given adequate information, like if you were told the total number of games they played you could solve it but with just this information it is unsolvable

Answer 84

aw man :((((((

Answer 85

None of these equations intersect thus, you cannot apply system of equations

Answer 86

wait i think u can

Answer 87

they switch it up a bit: Ron bowls x games, plays y video games, and spends $22.50. Ed bowls y games, plays x video games, and spends $15.00.

Answer 88

look at what x and y represent

Answer 89

its different

Answer 90

you dont have adequate information sorry lol, I'm so tired and in exam study mode, I should have realized earlier. If you don't believe me you can consult someone else but I'm pretty much a 100% sure at this point.

Answer 91

you aren't given any indication of how many games they played in total thus you cannot solve this

Answer 92

ok :(

Answer 93

the equations you can deduce from this have the same slope but different intercepts thus they do not intersect at any point therefore system of equations are useless in solving this. This is unsolvable

Answer 94

ok thnx anyway ill ask my friend or teacher for help

Answer 95

Well they will just tell you the same thing I told you but whatevers