Mathematics 19 Online
OpenStudy (anonymous):

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

OpenStudy (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.

OpenStudy (anonymous):

I am still confused. I am sorry

OpenStudy (sandra):

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

OpenStudy (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

OpenStudy (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

OpenStudy (sandra):

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

OpenStudy (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

OpenStudy (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

OpenStudy (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

OpenStudy (sandra):

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

OpenStudy (sandra):

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

OpenStudy (sandra):

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

OpenStudy (sandra):

ok, so now we KNOW x=20

OpenStudy (sandra):

and then we substitute it back into either of our equations

OpenStudy (sandra):

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

OpenStudy (sandra):

and then y = 27

OpenStudy (sandra):

does that make more sense?

OpenStudy (sandra):

ok so we had 2x + 7 = 47

OpenStudy (sandra):

we need to subtract 7 from both sides

OpenStudy (sandra):

so 2x = 40

OpenStudy (sandra):

and now we divide each side by 2

OpenStudy (sandra):

so x=20

OpenStudy (anonymous):

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

OpenStudy (sandra):

exactly

OpenStudy (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

OpenStudy (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

OpenStudy (sandra):

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

OpenStudy (sandra):

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

OpenStudy (anonymous):

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

OpenStudy (sandra):

ok sure

OpenStudy (anonymous):

do i post here or on the left?

OpenStudy (sandra):

on the left =)