the second of two numbers is 7 more than the first. their sum is 47. Find the numbers
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.
I am still confused. I am sorry
ok so you're trying to translate this word problem into two equations
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
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
or in other words, y = x + 7, with y being the second number, and x being the first
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
the next step, once you have as many equations as you do variables to solve for, is to start substituting one into the other
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
so x + y = 47, substituing x + 7 for y, we get x + x + 7 = 40
errr sorry, x + (x + 7) = 47
if you keep solving this, then we see that 2x + 7 = 47 , 2x = 40, x = 20
ok, so now we KNOW x=20
and then we substitute it back into either of our equations
so since x + y = 47, and we know x = 20, we see 20 + y = 47
and then y = 27
does that make more sense?
ok so we had 2x + 7 = 47
we need to subtract 7 from both sides
so 2x = 40
and now we divide each side by 2
ok. so we sub. 7 to get X by itself?
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
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
and this property holds true for any operation on equal values (the two sides of an equation)
as long as I do the same operation to both sides, I know they're still equal
can i post another one? I will try and work on it and see if i get it right?
do i post here or on the left?
on the left =)
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