Question

A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 40
pounds each, and the small boxes weigh 15
pounds each. There are 135
boxes in all. If the truck is carrying a total of 3650
pounds in boxes, how many of each type of box is it carrying?

Answer 1

please help :)

Answer 2

@MattAlva98

Answer 3

i am doing my math

Answer 4

okay.

Answer 5

@mathmate

Answer 6

Have you already done systems of two equations?

Answer 7

this is hard

Answer 8

no... not sure how to set that up

Answer 9

40x +15y=135??

Answer 10

So you have already learned system of two equations, right?

Answer 11

yes

Answer 12

Ok, do you want the normal way, or the easy way?

Answer 13

idc i just really neeed to get this question answered ,

Answer 14

I will set up both, will let you choose which one to use, but I will not solve it for you. You can choose to give me your answer to check if you want.
Do you want me to go ahead?

Answer 15

okay yes

Answer 16

Method 1:
Let x=number of heavy boxes at 40 lbs ea.
y=number of small boxes at 15 lbs ea.
Total number of boxes = x+y = 135 .....(1)
Total weight = 40x+15y = 3650 ......(2)
So you can solve for x and y in the above system of equations.

method 2:
Let x=number of heavy boxes at 40 lbs each
(135-x) = number of small boxes at 15 lbs each.
Total weight = 40x + 15(135-x) = 3650
Distribute and solve for x.

Do you have any question on the setups?

I will give you a third method in a post that follows.

Answer 17

x=65 y=70

Answer 18

so the small box is 65 and the large is 70?

Answer 19

Yes, try checking using 65*40+70*15=?

Answer 20

Good job!

Answer 21

thanks

Answer 22

You're welcome! :)

Answer 23

i have one more if you dont mind

Answer 24

@mathmate

Answer 25

Two mechanics worked on a car. The first mechanic worked for 10
hours, and the second mechanic worked for 5
hours. Together they charged a total of 1350
. What was the rate charged per hour by each mechanic if the sum of the two rates was 195
per hour?

Answer 26

Why don't you try your setup on this one, it's almost the same as the previous!

Answer 27

x+y = 1350 and 10x +5y=195?

Answer 28

is that right?

Answer 29

Almost, just two things.
Always define the variables used, so when you set up the equations you will not get confused.

Answer 30

So what do x and y stand for?

Answer 31

Define them before you set up equations!

Answer 32

x is for the numberof hours the first mechinic worked

Answer 33

y is for the second mechianic

Answer 34

If you reread the question and compare with your definitions of x and y, you will see a little problem, can you spot that?

Answer 35

uhh not really

Answer 36

"The first mechanic worked for 10
hours, and the second mechanic worked for 5
hours"
so you don't really need x=10 and y=5.
Think of x and y as numbers you need to find.

Answer 37

so is my first equation right just not the second?

Answer 38

Equations depend on what the variables x and y represent. I cannot say which one is right or wrong before we know what x and y stand for.
That is why we need to define x and y before setting up equations, agree?

Answer 39

okay

Answer 40

remember that charges are proportional to the number of hours worked and the rate.
So if the first one charges $x per hour and worked for 10 hours, his charge will be 10x dollars.

Answer 41

so if the mechinaic that worked 10 hours charged 10 a hour?

Answer 42

We don't know if he charged $10 an hour, that's why we need to solve the problem.

Answer 43

okay, i just need help setting up the equations i have it from there

Answer 44

Can you define your variables x and y, knowing the number of hours worked, and the total bill?

Answer 45

please this thing is timed i really need to get it answered ::(

Answer 46

im not asking for the answer just show me how to set up the equations again please

Answer 47

I am not even supposed to help you if this is timed, meaning this is a test.
But I will give you a last hint:
The only thing you don't know is the rate in $/hour.
So
Let x=rate for first person in $/hour, and y=rate for second person in $/hour.
Proceed as in the first question. You should have no problems with that.

Answer 48

not a test, it will log me out after a few minutes of not using it.

Answer 49

i got it
it was 75 and 120

Answer 50

thanks

Answer 51

Well, if you define the variables as above, you can give it a try with the setup.
Remember that defining the right variables is the most important step in the setup.

Answer 52

Yes, your answer is correct.
Did you guess?

Answer 53

no, i put the equations togehter??

Answer 54

Good, keep it up, and congratulations!