Question 693941: the second of two numbers is 7 more than the first. Their sum is 47. Find the numbers. Found 2 solutions by JBarnum, RedemptiveMath:Answer by JBarnum(2146) (Show Source):
You can put this solution on YOUR website! Let us nominate two variables to stand for two numbers (1 each). Let x equal the first number and y equal the second. The problem gives us the first characteristic of the numbers: The second number, or what we have called y, is 7 more than the first, or what we have called x. In mathematical language, we could say this:
y = x + 7.
Y is (equals) 7 more (+7) than x. This would be our first equation. Now we need to find the second by looking at the second characteristic. The problem states that their sum is 47. Again, in mathematical language:
x + y = 47.
X + y (sum of x and y or sum of the two numbers) is (equals) 47. Now we can use substitution to find x. The first equation says that y = x + 7, so we can plug what y equals here into the second equation x + y = 47 to find x:
x + y = 47
x + (x + 7) = 47 (substitution y = x + 7)
2x + 7 = 47 (combine like terms)
2x = 40 (subtract each side by 7)
x = 20 (divide each side by 2 to get x by itself).
Now we have found the first number to be 20. All we need to do to find the second if plug what we have found for the first into either equation:
x + y = 47
20 + y = 47 (substitution x = 20)
y = 27 (subtract each side by 20 to get y by itself)
OR
y = x + 7
y = 20 + 7 (substitution x = 20)
y = 27 (combine like terms).
The first number is 20 and the second number is 27. The second is 7 more than the first, and they add up (sum) to equal 47.
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