Question

the second of two numbers is 7 more than the first. their sum is 47. Find the numbers

Answer 1

x+y=47, x-y = 7 means that if we add the two questions, 47 + 7 = x + y + x - y = 2x = 54. Then x = 27 and y = 20.

Answer 2

I am still confused. I am sorry

Answer 3

ok so you're trying to translate this word problem into two equations

Answer 4

the point being, that two solve a problem with two variables (in this case the two numbers), you need two equations that have both variables in them

Answer 5

so for the first part of the word problem, it's saying that we have two numbers, and one of the numbers is 7 greater than the other

Answer 6

or in other words, y = x + 7, with y being the second number, and x being the first

Answer 7

now the second piece of information tells you that when you add both together, they equal 47. so you can write that as an equation like this:
x + y = 47

Answer 8

the next step, once you have as many equations as you do variables to solve for, is to start substituting one into the other

Answer 9

so in this case, why don't we choose the first equation, that is, y = x + 7, and "substitute" y into the second equation. That is, we can replace all the "y" variables in the second equation (there's only one), with x+7

Answer 10

so x + y = 47, substituing x + 7 for y, we get x + x + 7 = 40

Answer 11

errr sorry, x + (x + 7) = 47

Answer 12

if you keep solving this, then we see that 2x + 7 = 47 , 2x = 40, x = 20

Answer 13

ok, so now we KNOW x=20

Answer 14

and then we substitute it back into either of our equations

Answer 15

so since x + y = 47, and we know x = 20, we see 20 + y = 47

Answer 16

and then y = 27

Answer 17

does that make more sense?

Answer 18

ok so we had 2x + 7 = 47

Answer 19

we need to subtract 7 from both sides

Answer 20

so 2x = 40

Answer 21

and now we divide each side by 2

Answer 22

so x=20

Answer 23

ok. so we sub. 7 to get X by itself?

Answer 24

exactly

Answer 25

the reason we can do that is because we know if you subtract anything from two equal values (e.g. an eqation like 2x+7 = 47), we know that they are STILL equal - since we did the same operation to both values

Answer 26

i.e. if I have two baskets that have the same number of oranges in them, and I take out two oranges from each, regardless of how many they started with, they still have the same number

Answer 27

and this property holds true for any operation on equal values (the two sides of an equation)

Answer 28

as long as I do the same operation to both sides, I know they're still equal

Answer 29

can i post another one? I will try and work on it and see if i get it right?

Answer 30

ok sure

Answer 31

do i post here or on the left?

Answer 32

on the left =)