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

- anonymous

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

- katieb

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- anonymous

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.

- anonymous

I am still confused. I am sorry

- sandra

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

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- sandra

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

- sandra

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

- sandra

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

- sandra

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

- sandra

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

- sandra

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

- sandra

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

- sandra

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

- sandra

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

- sandra

ok, so now we KNOW x=20

- sandra

and then we substitute it back into either of our equations

- sandra

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

- sandra

and then y = 27

- sandra

does that make more sense?

- sandra

ok so we had 2x + 7 = 47

- sandra

we need to subtract 7 from both sides

- sandra

so 2x = 40

- sandra

and now we divide each side by 2

- sandra

so x=20

- anonymous

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

- sandra

exactly

- sandra

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

- sandra

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

- sandra

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

- sandra

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

- anonymous

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

- sandra

ok sure

- anonymous

do i post here or on the left?

- sandra

on the left =)

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