Question

algebra question please help:
sam buys 10 t shirts and lilly buys 4 sweatshirts both pay the same amount but both have different prices and the total of both 10 t shirts and 4 sweatshirts is 230$ what is the price of each sweatshirt?

Answer 1

okay so first you are going to want to make equations with the info you know. You will have 2 equations. Any ideas on 1?

Answer 2

is it 230+10x?

Answer 3

ugh no thats wrong no i really don't know

Answer 4

Okay well we can figure out a price equation and a number equation (number of shirts)

Answer 5

is it right?

Answer 6

so first we can pick 2 variables for sweatshirts and tshirts. how does s and t sound?

Answer 7

Not exactly.

Answer 8

great)

Answer 9

Okay cool. We can start with the cost equation first since that one tends to be easier. We know from the info given that 10 tshirts and 4 sweatshirts cost $230 right?

Answer 10

yes

Answer 11

So we can make an equation using those numbers and using the variables t and s which will represent the cost of 1 tshirt or 1 sweatshirt (depending on which variable it is). 10t+4s=230.

Answer 12

okay im with u

Answer 13

u know i tried this but then i didnt know what to do

Answer 14

okay good :) does that all make sense why you would set it up that way?

Answer 15

yes

Answer 16

Lol well its good you tried! We all get stuck sometimes :/

Answer 17

yes i know :(

Answer 18

Okay so the other info we have left is that 10 tshirts and 4 sweatshirts cost the same, right?

Answer 19

not each one costs the same but when they purchased 10 t shirts it was the same as 4 sweatshirts

Answer 20

the total of 10 tshirts is the same total of 4 sweatshirts (meaning sweatshirts will be more expensive if you think about it. You get less sweatshirts than tshirts but it all totals up to the same amount)

Answer 21

ye s yes

Answer 22

yes yes thats true

Answer 23

Yup! That's a good catch. So when we write the equation we will need to make sure that we include 10 and 4 and not just 1 like you said.

Answer 24

yes

Answer 25

So if they both cost the same amount, you could set them equal right? Does this part make sense?

Answer 26

10t=4s

Answer 27

yes

Answer 28

Because the 10t is the COST, not the number of shirts. and 4s is the COST also (since t and s are prices per one shirt). And we know the costs are EQUAL. So therefore we can write that equation, good?

Answer 29

yes yes

Answer 30

awesome. Here are our 2 equations:
\[10t+4s=230\]
\[10t=4s\]

Answer 31

yes great :)

Answer 32

Any ideas on what we do with this excellent info we have? :D

Answer 33

no idea :(

Answer 34

but i understand everything till now

Answer 35

Okay don't worry :)
The next goal is to solve for a variable! You can pick which you want to solve for first, t or s. We will eventually find both anyways. Which would you like to solve for first?

Answer 36

t

Answer 37

Okay. So then we will need to get only t in an equation.
10t+4s=230 <--- we can use this equation to solve for t. (you could use the other but this is one is easier in my opinion)
10t=4s <--- here we have it telling us that 4s=10t. That means we can do...
\[10s+10s=230\] (this is the first equation just with the substitution)

Answer 38

Do you see how i got that?

Answer 39

whattt

Answer 40

why 10s +10s

Answer 41

oooh my bad, I meant 10t+10t!!

Answer 42

not s lol

Answer 43

Does that clear it up, or do you want me to explain still?

Answer 44

wait why did we do this equation ugh sorry

Answer 45

how did u get it

Answer 46

10t+4s=230

10t=4s

This is the info we have.
10t+*4s*=230 we need to get only t's in the equation, BUT there is a sneaky *4s* in there. It's no biggie though because in our other equation, it tells us that 10t=*4s* which is the same as *4s*=10t. If 4s is the same thing as 10t then you can plug in 10t for 4s! Because they equal the same thing, so the value is the same, just a different way of writing it :D It won't change the equations value, just different variables, but it's still equal :)

Answer 47

10t+10t=230

Answer 48

ohhhhh okay so basically u subistusted because they are equal

Answer 49

Exactly!!

Answer 50

Now you can solve for t because it's the only variable in the equation. Let me know what you get

Answer 51

so its 20t=230

Answer 52

so its 11.5

Answer 53

Perfect, good job! :D So if t (price of 1 tshirt) is $11.50, we can plug that info into either equation for t and find the price of a sweatshirt (s).

Answer 54

I should've reread your question, it only wants to know the price of a sweatshirt, not the tshirt. But more info is never a bad thing :P

Answer 55

yes hahaha i was going to tell u buts its my bad

Answer 56

10t+4s=230
10(11.5)+4s=230

OR you can do this one
10t=4s
10(11.5)=4s

Answer 57

Lol no problem xD Extra practice is good

Answer 58

let me solve it and tell u the answer

Answer 59

You can pick whichever one you want, you don't HAVE to solve for both, they should give the same answer

Answer 60

28.75

Answer 61

waiiitt u know i did it another way without doing equations and i had the same answer

Answer 62

You got it!! And how did you do it?

Answer 63

i divided 230/2 since they are equal then i got 115 then i did 115/10 which is 11.5 and 115/4 which is 28.7

Answer 64

Oh wow, that is a much easier and faster way and it definitely works! Super smart of you!!

Answer 65

yes but i think your way is better since its algebra and we need formulas there u know

Answer 66

your so smart i really like how u explain everything really detailed so smart way to go !

Answer 67

Yes sadly :C But knowing multiple ways of doing it is always a good thing, so great job!

Answer 68

Aww thank you! I hope it helped :)

Answer 69

thank you and i really appreciate your help i really wanted someone to help and u were there so i really appreciate that

Answer 70

Anytime!!! Good luck with the rest of your work :D

Answer 71

it helped a lot thank you again :)

Answer 72

thank you