Question

The math club raised money for its spring banquet by washing vehicles. The club charged $3 per car and $5 per truck. The club earned a total of total of $ 550 for washing 122 cars and trucks combined. How many cars did the club wash?

Answer 1

So, you have to form a system of equations

Answer 2

this is a system of equations

3 dollars per car means 3c (c being cars washed) and 5 dollars per truck washed means 5t (t being trucks washed) and that total is 550....so

3c + 5t = 550

you know they washed 122 cars (c) and trucks (t) combined...so

c + t = 122

so you have

3x + 5t = 550
c + t = 122

do you know how to solve a system of equations?

Answer 3

sorry should be 3c in that first equation!!***

Answer 4

I mean, I am pretty sure my Algebra teacher taught this in class. But, I just can never remember or comprehend what she teaches. Mathematics is my total weakness :(

Answer 5

good explaining johnweldon :)

Answer 6

thank you @kelliegirl33 :)

and okay @lovetostudy we'll walk through this step by step :)

Answer 7

so we have

3c + 5t = 550
c + t = 122

what we want to do.....is solve for the number of CARS washed correct?

this means....that you eventually want to solve for "c"

take

c + t = 122

solve for t here
to isolate t (get by itself)....you would subtract "c" from both sides...... and get

t = 122 - c right?

with me so far?

Answer 8

yes.

Answer 9

we're solving for C (cars) by isolating T (trucks) , correct?

Answer 10

CORRECT!

so not...you take that t.....and what it equals (122 - c)...and plug it into that first equation

3c + 5t = 550

and plug in (122-c) wherever you see a "t" so

3c + 5(122 - c) = 550

still with me?

Answer 11

***notice that the ONLY varible left.....is C...which IS what we're solving for...that is exactly why we isolate T in the first part :)

Answer 12

Would we need to use distributive property next?

Answer 13

yes indeed we would :)

so what does our equation look like after that?

Answer 14

3c+610=550?

Answer 15

you forgot the 5 x -c

Answer 16

close....what is the distributive property?

where you have

5(122 - c)
you would multiply the 5 by 122....AND THEN 5 times -c as well right?

Answer 17

I know I have to do something with the -c that's in the parentheses, but I forgot :(

Answer 18

Yes.

Answer 19

so you do exactly that

5 times 122....is the 610
5 times -c is?

Answer 20

-5c

Answer 21

perfect!

so altogether we have

3c + 610 -5c = 550

where would we go from here?

Answer 22

Um, like terms? :o

Answer 23

yes! ....meaning?

Answer 24

we add 3c + -5c

which would equal ... -2c?

Answer 25

exactly!

so

-2c + 610 = 550

what now?

Answer 26

We subtract 610 from itself so it cancels out and then subtract that from 550?

Answer 27

mmhmmm...whick leaves us with?

Answer 28

which*

Answer 29

-2c+610=550
-610 -610
then,
-2c -60
----- = ------
-2c -2c

the answer is ... 30? :D

Answer 30

very good! :)

but for future reference....we dont divide -2c and -60 by -2"c" we just divide it by -2

if we divide them by -2c we'll have

-2c = -60
----------
-2c -2c

1 = -60/-2c

not the same

just for the future....but very good :)

Answer 31

Ohh, ahha. Sorry, Typo. I was doing it on a loose sheet of paper and mistakenly included the variable. Oops.

Answer 32

not a problem ..just wanted to make sure! :)

very good work @lovetostudy :)

Answer 33

Thank you :) Just one more question, (sorry to bother)

If my final answer is 30, then why does it not appear as an answer choice on my worksheet? :o That's very odd.

Answer 34

what are your answer choices?

Answer 35

1) 36
2) 50
3) 72
4) 86

Answer 36

hang on let me double check

Answer 37

ummm...no it should definitely be 30 cars....which corresponds to 92 trucks...and to check it

3(30) + 5(92) = 550
90 + 460 = 550

550 = 550

its correct...so your answer choices must be wrong

Answer 38

let me get a different opinion first though

Answer 39

@jim_thompson5910 mind looking this over for me?

Answer 40

Okay :)

Answer 41

I'm getting c = 30 and t = 92 as well

so there has to be a typo somewhere

Answer 42

thank you very much @jim_thompson5910 :)

Answer 43

Thank you, Jim

Answer 44

yw

Answer 45

I'm guessing there IS a typo :o Thank you so so much John. You've really guided me to see the light at the end of the dark tunnel. Haha Greatly appreciate your guidance. :)

Answer 46

Oh!! It was my mistake all along . The total earned was 510 instead of 550 -.-

Answer 47

ok so one of those answer choices is correct assuming the 550 changes to 510

Answer 48

Yes.

Answer 49

what do you get for c this time

Answer 50

right do this again the same way...but with 510

Answer 51

It's 50. I found the answer thanks to your help & refreshing my mind of how to solve these types of problems :D

Answer 52

great job :)

Answer 53

Oh my goodness, I am so proud of myself. I would've never done it without you :) and Jim :)

Answer 54

lol didn't do anything really, but yw

Answer 55

lol sometimes a second opinion / confirmation is all the help you need Jim!

Answer 56

hmm true, but you did most of the work

Answer 57

So true.