Question

One type of candy sells for $2 per pound, and another type sells for $3 per pound. An order for 18 pounds of candy costs $47. How much of each type of candy was bought?

Answer 1

So can you think of a way to make an equation for the total price of candy and the total weight of the candy if the weight of candy 1 is X and the weight of candy 2 is Y?

Answer 2

It might help to list out all the information you know and try to find what you don't know. For instance you have:

Total weight of candy: 18 pounds
Candy 1 per weight: 2 dollars/pound
etc...

Answer 3

uummmmm

Answer 4

no I can't

Answer 5

Start out small, tell me what 4 values the problem gives you. I already gave you 2.

Answer 6

2/1b, 3/1b, 18 pounds, $47 dollars.

Answer 7

Alright, so if candy 1 is 2 dollars per pound, then that means that 1 pound of that candy is 2 dollars, right? 2 pounds of that same candy would be 4 dollars, and 3 pounds would be 6 dollars. So the total price is based off of the weight of the candy.

So if we say the weight of candy 1 is X, then we can say 2x=P is the price of just the first candy. Can you come up with an equation that describes the weight of the other candy based on its weight if you use Y instead of X?

Answer 8

3y=P

Answer 9

Boom, perfect. Now you know the total price, 47 dollars. That's the sum of both of those prices.

So now are you able to make an equation for the total price and total weight?

Answer 10

what do I do?

Answer 11

If not, that's ok, I'm just trying to help you understand because it'll be harder to do this on a test.

Answer 12

So 2x is the price of candy 1 and 3y is the price of candy 2 and you're given the total price, 47 dollars.

2x+3y=47

now what are x and y? The weights, and remember you were given the total weight of the candy is 18. Can you make an equation for the total weight of the candy using x, y, and 18?

Answer 13

i have no idea

Answer 14

x is the weight of one candy, y is the weight of the other candy and 18 is the total weight of both candies combined. Think about it a little bit, how can you make an equation out of those 3 things?

Answer 15

I don't know

Answer 16

Which equation looks right to you:

x-y=18
x+y=18
xy=18
x/y=18

Answer 17

What problem are you having here? I'm not going to help you anymore if you don't tell me what's so hard about this.

Answer 18

x/y=18?

Answer 19

You think the weight of one candy divided by the weight of the other candy is the total weight? Why?

Answer 20

If I give you 10 pounds of one candy and 20 pounds of another candy, is the total weight of the candy a half pound or 30 pounds?

Answer 21

30

Answer 22

Write down the equation you used to figure that out and post it.

Answer 23

Instead of 10 and 20 pounds use x and y and instead of 30 pounds use 18

Answer 24

brb...dont go away

Answer 25

Kk I'll be here =D

Answer 26

ok. 2x+3y=47

Answer 27

2x+3x=18

Answer 28

2x+3y=47 that's the equation that tells you the total price. But you have 2 unknowns, so you need 2 different equations. So what is an equation for the total weight? Remember, the total weight is 18. What are the weights of the candies?

candy 1 is x
candy 2 is y
both candies is 18

Make that into an equation.

Remember in the example we did earlier,

Candy 1 is 10 pounds
Candy 2 is 20 pounds
both candies is 30 pounds

write out that as an equation

Answer 29

I don't get it, I've never been good at math.

Answer 30

You said it yourself. 20 pounds of candy plus 10 pounds of candy is 30 pounds of candy right?

so 20+10=30

But instead of 20 pounds, lets just say it's x pounds of candy, cause we don't know, and y pounds of candy for the other. Then both of those is 18 pounds. I know you can do it haha.

Answer 31

all I can think of is that half of 18 is 9

Answer 32

theres too many things that can =18

Answer 33

I don't even care anymore so thanks for your time and sorry I'm too stupid to figure it out

Answer 34

x+y=18

Answer 35

now you have 2 equations to solve for your variables.

Answer 36

Just rest on it a little bit. Part of math is that sometimes it's frustrating, but eventually you'll get it if you step away from the problem and come back to it.

Answer 37

Ok Im going to straight up give you the answer x=7, y=11.

Answer 38

meaning there are 7 pounds of 2 candy and 11 pounds of 3$ candy.

Answer 39

how do you know it's not 6 and 12?

Answer 40

Now I'll explain how I solved it.
So let x= Weight of 2 dollar candy and y= weight of 3 dollar candy. As the question states the total pounds of candy is x+y=18. Now thats one equation done. Lets make two equations so we can solve them both simultaneously. The price of his purchase was 47$. So the "price equation" would be 2x+3y=47. (As 2$ per pound therefore if we had 4 pounds it would cost 8 and likewise for the three dollar candy, 3*4 would = 12 so basically weight multiplied by cost will give you total cost.). Now lets solve these two equations simultaneously, 2x+3y=47 and x+y=18. Lets try getting rid of a variable by multiplying the bottom equation by 2. so now the bottom equation is 2x+2y=36 (multiplying everything in the bottom by 2). Great so now we can cancel out the x variable. as 2x-2x=0, 3y-2y=1y. So 1y=47-36. y=11 and if we plug y=11 into one of the equations lets do the easy one x+y=18 we will learn that x=7. So there we go. Problem solved.

Answer 41

and its not 6 and 12 because 6*2=12 and 12*3=36. 36+12=48 but in the question it says total cost was 47 and NOT 48.

Answer 42

If you need an elaboration/clarification just ask.

Answer 43

Thank you. :)