anonymous
  • anonymous
the second of two numbers is 7 more than the first. their sum is 47. Find the numbers
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • 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
  • anonymous
I am still confused. I am sorry
sandra
  • sandra
ok so you're trying to translate this word problem into two equations

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sandra
  • 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
  • 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
  • sandra
or in other words, y = x + 7, with y being the second number, and x being the first
sandra
  • 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
  • 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
  • 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
  • sandra
so x + y = 47, substituing x + 7 for y, we get x + x + 7 = 40
sandra
  • sandra
errr sorry, x + (x + 7) = 47
sandra
  • sandra
if you keep solving this, then we see that 2x + 7 = 47 , 2x = 40, x = 20
sandra
  • sandra
ok, so now we KNOW x=20
sandra
  • sandra
and then we substitute it back into either of our equations
sandra
  • sandra
so since x + y = 47, and we know x = 20, we see 20 + y = 47
sandra
  • sandra
and then y = 27
sandra
  • sandra
does that make more sense?
sandra
  • sandra
ok so we had 2x + 7 = 47
sandra
  • sandra
we need to subtract 7 from both sides
sandra
  • sandra
so 2x = 40
sandra
  • sandra
and now we divide each side by 2
sandra
  • sandra
so x=20
anonymous
  • anonymous
ok. so we sub. 7 to get X by itself?
sandra
  • sandra
exactly
sandra
  • 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
  • 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
  • sandra
and this property holds true for any operation on equal values (the two sides of an equation)
sandra
  • sandra
as long as I do the same operation to both sides, I know they're still equal
anonymous
  • anonymous
can i post another one? I will try and work on it and see if i get it right?
sandra
  • sandra
ok sure
anonymous
  • anonymous
do i post here or on the left?
sandra
  • sandra
on the left =)

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