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anonymous
 5 years ago
the second of two numbers is 7 more than the first. their sum is 47. Find the numbers
anonymous
 5 years ago
the second of two numbers is 7 more than the first. their sum is 47. Find the numbers

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0x+y=47, xy = 7 means that if we add the two questions, 47 + 7 = x + y + x  y = 2x = 54. Then x = 27 and y = 20.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I am still confused. I am sorry

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0ok so you're trying to translate this word problem into two equations

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0the 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
 5 years ago
Best ResponseYou've already chosen the best response.0so 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
 5 years ago
Best ResponseYou've already chosen the best response.0or in other words, y = x + 7, with y being the second number, and x being the first

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0now 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
 5 years ago
Best ResponseYou've already chosen the best response.0the next step, once you have as many equations as you do variables to solve for, is to start substituting one into the other

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0so 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
 5 years ago
Best ResponseYou've already chosen the best response.0so x + y = 47, substituing x + 7 for y, we get x + x + 7 = 40

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0errr sorry, x + (x + 7) = 47

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0if you keep solving this, then we see that 2x + 7 = 47 , 2x = 40, x = 20

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0and then we substitute it back into either of our equations

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0so since x + y = 47, and we know x = 20, we see 20 + y = 47

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0does that make more sense?

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0ok so we had 2x + 7 = 47

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0we need to subtract 7 from both sides

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0and now we divide each side by 2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok. so we sub. 7 to get X by itself?

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0the 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
 5 years ago
Best ResponseYou've already chosen the best response.0i.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
 5 years ago
Best ResponseYou've already chosen the best response.0and this property holds true for any operation on equal values (the two sides of an equation)

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0as long as I do the same operation to both sides, I know they're still equal

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can i post another one? I will try and work on it and see if i get it right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do i post here or on the left?
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