Question

Jessica invites some friends to a cowboy game. she purchases a suite at the stadium for $1,500. She also orders a $250 pizza hut package. Three other family members already had tickets to the game, but join for the pizza. If the prices were divided evenly between Jessica and her friends - and the cost was $57.58 per person - how many friends did Jessica invite to the game?

Answer 1

I want to know how to set up the problem.

Answer 2

like what equation do i use?

Answer 3

Hm. My intuition would be that you would add the cost of the suite + pizza package then divide by x and set that equal to the price per person

Answer 4

(1500+250)/x = 57.58

Answer 5

but that doesn't give me a whole number so that can't be it

Answer 6

what about the "three" family members?

Answer 7

the wording is throwing me off

Answer 8

i did not make it up, my teacher gave it to me and he probably modified it with different words so we would not cheat.

Answer 9

yeah it's not your fault, let me try and work something out

Answer 10

okay thank you ill wait patiently.

Answer 11

this is my best attempt

the 1500 suite is split between Jessica and her friends

the 250 pizza is split between Jessica, her friends, and her family

so if we divide total cost/total people for each part, we get 57.78

Answer 12

let x = the number of friends

Answer 13

1500/(Jessica + friends) + 250/(Jessica+friends+ 3 family members) = 57.78

1500(x+1) + 250/(x+1+3) = 57.78

this gives me x ~ 30

Answer 14

so jessica is x right?

Answer 15

x is the number of friends

Answer 16

Jessica + Friends= x+1

Answer 17

yeah, friends is x and Jessica is 1 person

Answer 18

ok i get it know because the problem wants us to find the number of friends right

Answer 19

yes

Answer 20

but wait why did you multiply 1500(x+1) and not divide?

Answer 21

there should be a division sign between them sorry

Answer 22

ok

Answer 23

i want to do this by hand and not by calculator how will i start with (1500/x+1)+(250/x+1+3)=57.78?

Answer 24

does 250/x+1+3 simplify to 250/x+4 right?

Answer 25

yes

Answer 26

you would just make of the denominators the same by finding the lcd

Answer 27

*both of the denominators

Answer 28

how do i do that?

Answer 29

your denominator on the left is (x+1)

the denominator on the right is (x+4)

you would multiply the left denominator by (x+4)
and the right denominator by (x+1)

Answer 30

that will make both denominators (x+1)(x+4)

Answer 31

then, you have to perform the same operation to the numerators to keep the fractions equivalent

Answer 32

so is it 1500+250/(x+1)(x+4)?

Answer 33

you also have to perform the same operations to the numerators

Answer 34

so (x+1)(x+4)* the numerators?

Answer 35

1500(x+4)

Answer 36

pretend those lines are fraction bars

Answer 37

okay.

Answer 38

then add them together

Answer 39

wait i am confused.

Answer 40

why didnt you multiply 1500 time x+1?

Answer 41

times*

Answer 42

1500/(x+1) + 250/(x+4) are your original fractions

you multiply the numerator and the denominator of 1500/(x+1) by (x+4) to convert the denominator to (x+1)(x+4)

there would be no point in multiplying it by (x+1) since that's already in the denominator

Answer 43

ok

Answer 44

so like...

Answer 45

(x+4) 1500 (x+1) 250

Answer 46

@sillybilly123 can you tell me if I am interpreting this problem correctly?

Answer 47

wow this thing came out ugly lol.

Answer 48

can you try using the "equation" button perhaps?

Answer 49

ok sorry i am new

Answer 50

let me try and solve it

Answer 51

missing info unless you make assumptions

Answer 52

yeah, I made my best attempt based on my interpretation of the problem

Answer 53

\[(1750x+6250)/(x+1)(x+4)\]

Answer 54

i mean, Jessica is a "person" and she cannot end up paying a flat rate as she paid for the suite

Answer 55

i know but i guess my teacher does not like to have good grammar or something is wrong with his printer.

Answer 56

so what do i do next?

Answer 57

you would set that equal to 57.58 and solve for x

Answer 58

multiply (x+1)(x+4) times 57.78? and then solve for x?

Answer 59

(1750x+6250) = 57.58(x+1)(x+4)

if that's what you mean

Answer 60

yes, is that correct?

Answer 61

yes

Answer 62

expand the Right hand side using foil and then combine like terms

Answer 63

yeah

Answer 64

I would leave out the 57.58 until the very end after you have finished expanding (x+1)(x+4)

Answer 65

then you would multiply every term of the expansion by 57.58

Answer 66

ok

Answer 67

1745x+6250=x^2?

Answer 68

6246*

Answer 69

1745x+6246=x^2

Answer 70

I'm not exactly sure what you're doing ;-;

Answer 71

you said to multiply 57.78 at the end

Answer 72

start by expanding this (x+1)(x+4)

Answer 73

1750x+6250=x^2+5x+4?

Answer 74

1750x+6250=(57.58)(x^2+5x+4)

Answer 75

ok

Answer 76

then distribute the 57.58

Answer 77

1750x+6250=57.78x^2+288.9x+231.12?

Answer 78

good now combine like terms

Answer 79

they are already combined, or are they not?

Answer 80

i just need to solve for x right?

Answer 81

move everything to one side of the equation

Answer 82

ok

Answer 83

then apply the quadratic formula

Answer 84

-7869.667713?

Answer 85

to have that amount of friends she must be on drugs or something

Answer 86

let's back up a bit

Answer 87

ok to where?

Answer 88

to here:

1750x+6250=57.78x^2+288.9x+231.12

Answer 89

subtract 1750x from both sides

Answer 90

ok wait let me erase something because my paper is getting full

Answer 91

0=57.78^2-1461.1x-6018.88?

Answer 92

yeah now apply the quadratic formula

Answer 93

okay

Answer 94

x~28.893?

Answer 95

so 29?

Answer 96

yup

Answer 97

[it's a bit off 29 because of rounding error]

Answer 98

anyway, I have no guarantees this is the answer but again this was my best attempt

Answer 99

alright thank you very much anyways, i probably gave you a headache, because i am having one. have a great day.