Question

Please Help!! The number of items on two grocery lists differs by 7. The total number of items is 33. How many items are on each list?

Answer 1

Hello! How far have you got with this question, so far?

Answer 2

umm no where? i just started it

Answer 3

i dont know where to start or end

Answer 4

Okay, that's fine. Let's start by choosing a couple of variables (maybe call them x and y, or A and B). Any idea what they might represent?

Answer 5

(It's okay if you have no idea!)

Answer 6

okay lets do a and b.... and they represent the grocery list right?

Answer 7

That's right, "a" would be the number of items on one list, and "b" would be the number of items on the other list.

Answer 8

alright then what?

Answer 9

Let's try writing down an equation (with a and b) to show that the total number of items is 33. Any idea how we might do that?

Answer 10

(It's okay if you don't know!)

Answer 11

well thats kinda my problem i have trouble trying to come up with the equatiion... i dont know

Answer 12

Okay, no problem! The number of items in the first list is "a", and the number of items in the second list is "b". If the total number of items is 33, that means that adding up "a" and "b" will give you 33. Does that help?

Answer 13

so your saying a plus b equals 33??

Answer 14

Exactly! That's our first equation: a + b = 33.

Answer 15

Let's be clear: "a" isn't the name of the first list. It's a number: the number of items in the first list (e.g. 10).

Answer 16

Does this make sense, so far?

Answer 17

ohhh okay i think so

Answer 18

Great! Let's try the second clue then: we're told that the number of items in the two lists differs by 7. Any idea how we might write this as an equation?

Answer 19

a+b-7=33?

Answer 20

You're on the right track. Forget about the 33 for now. All we care about is that the first and second list differ by 7.

So maybe the first list has 1 item and the second one has 8, or maybe the first list has 10 items and the second list has 17, or maybe the first list has 100 items and the second list has 107.

If that makes sense, maybe try again with writing down an equation?

Answer 21

(If that doesn't make sense, that's not a problem!)

Answer 22

im not sure......A-7+B? what you say makes sense but im not sure about the equation

Answer 23

Oooh, that's really close :) I think you might have mistyped something, cos an equation needs an equals sign!

Answer 24

no i thought we were forgetting about 33 A-7+B= 33 ?

Answer 25

Yep, we're ignoring the 33 for now. All we're trying to do is to turn this sentence into an equation: "The difference between a and b is 7."

Answer 26

-7+a+b=33 i dont know the equation at all :(

Answer 27

Okay, see if this makes sense:
a - b = 7

Answer 28

but i thought we were adding a + b?

Answer 29

That was the first sentence.
"The total number of items is 33" means: a + b = 33.

Now we're looking at the second sentence:
"The difference between the two numbers is 7" means: a - b = 7.

Answer 30

okay i understand what now?

Answer 31

Well, now we've got two equations (maybe you call them "simultaneous equations" at school?), and we'd like to solve them. Have you seen this kind of problem before?

Answer 32

If not, I can walk you through it :)

Answer 33

i dont think so? could you walk me through please??

Answer 34

Okay, there are two ways to solve equations like these. One method is called "substitution" and the other is called "elimination". Have you seen either of these before? (If not, I'll decide which one to use!)

Answer 35

i think substitution but im not sure

Answer 36

Okay, there are two steps in this method. We'll start by taking the first equation ( a+b=33 ) and rearrange it so that one of the letters (let's say "a") is by itself on one side. Any idea how we might do this?

Answer 37

no i dont think so..?

Answer 38

Okay, right now we have "a" and "b" on the same side:. We need to get rid of the "b" from the left hand side.