Mathematics 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 =)

Latest Questions SaltTheLoser: Does anyone want to do some edits?
12 minutes ago 12 Replies 0 Medals mohd: evaluate the closed line integral of h about the rectangular path
2 hours ago 4 Replies 0 Medals mohd: evaluate the closed line integral of h about the rectangular path
2 hours ago 0 Replies 0 Medals XxNoodlexX: How many chapters are too many for a book?
1 hour ago 78 Replies 4 Medals payton: thx to everyone who edited for me i will use your edits evey now and then
2 hours ago 17 Replies 1 Medal SaltTheLoser: How do you make edits?
3 hours ago 10 Replies 1 Medal Lexya: How do I make music with an egg and a toothpick
1 hour ago 25 Replies 3 Medals xxcoffee: who wanna edit a pic for me.even doe im ugly
4 hours ago 0 Replies 0 Medals jakfishman: i just wanna see who want to edit a pic of me
4 hours ago 0 Replies 0 Medals Denis: Who wants to uhm edit my doggo?
4 hours ago 5 Replies 0 Medals