Question

PLEASE HELPPPPPPPPPPPPPPPPPPPPP MY MIND IS ABOUT TO BLOW UP !!!

A certain dealership has a total of 100 vehicles consisting of cars and trucks. 1/2 of the cares are used, and 1/3 of the trucks are used. If there are 42 used vehicles altogether, how many trucks are there?

Answer 1

half of the cars*

Answer 2

i know the answer i just need to know how to get the answer

Answer 3

make them into a series of two equations

Answer 4

100= c+t
42 = 1/2c + 1/3t

Answer 5

can you solve that?

Answer 6

whoa nice..... lemme write that down

Answer 7

let the number of cars be x
therefore trucks = x-100
x/2+(100-x/3)=42
3x+200-2x/6=42
x=42*6-200
x=252-200
x=52

Answer 8

hey its not 52....

Answer 9

zimmah whats the next step

Answer 10

x is 52
trucks=100-52=48

Answer 11

He didn't say that the number of used cars was 52. Read the solution, he just found how many cars.......All you need to do is take half of that to find the used cars.

Answer 12

make the both equations so that you can subtract them from each other to remove C.

So, in that case, if you multiply the equation of 1/2c+1/3t=42 by 2, than you get c+2/3=84 (which is still the same) but now you can subtract this from the other equation.

Then you get an equation that only contains t and a number. So that way, you can know t.

Answer 13

can you explain to me how you cam across that equation?

Answer 14

c+2/3t=84 obviously, made a typo

Answer 15

1/2c+1/3t=42 you mean?

Answer 16

yea

Answer 17

that's the amount of used vehicles, since 1/2 of the cars is used, and 1/3 of the trucks is used.

And we know that together they are 42, because that was a given.

Answer 18

so what comes next?

Answer 19

In most of this type of question, you really have to puzzle a bit how you can best manipulate the data to get the information you need to solve it.

Answer 20

if you have two equations with both the same two unknowns (like you have here) one of the easiest methods is trying to erase one of the values from the equation.

There is another way (substitution), if you think that's easier.

But this way is just multiplication and subtraction.

We have 100 = c+t and
42 = 1/2c + 1/3t

we can easily erase the c by multiplying the second equation by 2, so that that equation also has a whole c, like the first.

If you then just simply subtract the whole equation from the first, you'll have an equation that has a number on one side, and a fraction of t on the other side.

That way, you know the total number of trucks. (and by extension, cars).

Answer 21

hmmmmm okay can you go into the steps?

Answer 22

100 = c+t
84 = c + 2/3t -
---------------------
16 = 1/3t

t = 3*16 = 48

Answer 23

notice how the c cancels itself out

Answer 24

also, since the first equation states 100 = c+t and you now know t, you also immediatly know that c must therefore be 52 (because 100-48 = 52)

Answer 25

yes

Answer 26

how did u get that 84?

Answer 27

and whered the 2/3 come from?

Answer 28

well, we had two equations to start with right?

Answer 29

And both of them have not 1, but two unknown values. Which on their own, makes them impossible to solve.

Answer 30

but together, you can use them to erase one of the unknown values (in this case i chose c, because that was the most logical thing to do in this case, but i might as well have chosen to erase t instead).

Answer 31

But since you have to either subtract or add (sometimes you have a negative value in one of the equations, then you must add instead). It will only really erase something if one of the values is the same. Therefore i had to multiply the whole equation by 2, before subtracting.

Answer 32

which equation is that?

Answer 33

If used this instead
100 = c+t
42 = 1/2c + 1/3t -
---------------------
58 = 1/2c+1/3t

then i would not be any better off

Answer 34

because then i still know nothing about c or t

Answer 35

ohhhh okay

Answer 36

for that reason, i multiplied 42 = 1/2c + 1/3t by 2

so 2*42 = 2*(1/2c) + 2*(1/3t)

Answer 37

What i did was \[42/\frac{ 1 }{ 3 }=126\]

Answer 38

then i divided 126/.5 and I got 252

Answer 39

is that wrong?

Answer 40

yes, that's wrong because 42 is the total number of used vehicles, not the number of used trucks.

Answer 41

so you can't just multiply 42 by 3

Answer 42

and especially not multiply it again by 2. Your number is much too big

Answer 43

i divided

Answer 44

dividing by a fraction is the same as multiplying by the opposite of that fraction.

try it out, 42*3 = 126 while 42/\(\frac{1}{3}\)=126 as well

Answer 45

well why did you multiply it by 2?

Answer 46

how else would you get rid of the c?

Answer 47

i dont understand that process.... how do u get rid of the c by multiplying it by 2?

Answer 48

you have two equations 100= c+t and 42 = 1/2c + 1/3t

in order to solve them, you have to get rid of either c or t.

Answer 49

because c - c = 0 but c - 1/2 c = 1/2c

Answer 50

since the second equation has 1/2c, we have to multiply it by 2, otherwise we can't get c-c=0

Answer 51

There is also another way, maybe that one is more your style.

Answer 52

yea this one is a bit confusing....

Answer 53

i wish i understood where u got that 2 from

Answer 54

we have 100= c+t and 42 = 1/2c + 1/3t

so to get rid of c this time we will express c as a function of t.

so we move the c in 100=c+t to one side, and the rest to the other

so c = 100-t (it's the same as 100=c+t, just in a different order)

Answer 55

okay

Answer 56

knowing that, we can use that in the second equation.

1/2*c + 1/3t = 42

since the other equation tells us c = 100-t, we can switch c out for 100-t, so let's do that.

don't forget to use brackets!

1/2*(100-t) + 1/3t = 42

now let's solve the brackets first

1/2*100 = 50 and 1/2*t is just 1/2t

so 50-1/2t+1/3t = 42

Answer 57

i think you can solve t from there

Answer 58

workin on it now

Answer 59

it's a bit more work than the method i used, but at least (hopefully) you can see what is happening here.

Answer 60

do i divide?

Answer 61

lol he is doing the samethning which i did

Answer 62

42 divided by .5?

Answer 63

sorry im so slow at this

Answer 64

how did you arrive at 42 divided by 0.5 exactly?

Answer 65

hey u there?

Answer 66

yes i am i was lookin over the steps on top

Answer 67

if you want to solve 50-1/2t+1/3t = 42 probably best to first make 1/2t+1/3t into one fraction

Answer 68

lets start from the beginning
let the total number of cars be x

Answer 69

total number of ars is 100 no?

Answer 70

please don't confuse the two methods with each other, they are both correct but very different from each other. Use only the second one, because the first one is just not for you apparently. Nothing to be ashamed of, just don't use it.

Answer 71

vehicles*

Answer 72

okay

Answer 73

cj you take this over? I'm helping someone else right now

Answer 74

THANK YOU ZIMMAH

Answer 75

understand the question first we have total 100 vehicles

Answer 76

yea

Answer 77

so lets say out of 100 we have x number of cars

Answer 78

yea

Answer 79

so trucks wud be 100-x

Answer 80

yea

Answer 81

now the next step in the question its mentioned that 1/2 of the cars are used

Answer 82

yes

Answer 83

so 1/2 (x)=x/2

Answer 84

why is it x/2?

Answer 85

bc 1/2 cars are used and we termed x as the number of cars. so out of x 1/2 cars are used. now multiply 1/2 by x and ull get the ans as x/2

Answer 86

oh hmmm okay

Answer 87

u understood this much ryt

Answer 88

yes

Answer 89

now we have 100-x total amt of trucks and out of that 1/3 trucks are used so now wat wud be the equation foh trucks

Answer 90

x/3?

Answer 91

no...we have 100-x no of trucks so we wud multiply it with 1/3

Answer 92

x/3 + x/2

Answer 93

wat is x in our equation

Answer 94

the number of used trucks

Answer 95

scroll up ull see x=total number of cars
100-x=total number of trucks

Answer 96

oh we're looking for cars? okay

Answer 97

no we are looking for trucks

Answer 98

read the question.