SOLUTION: The sum of two numbers is 56. If the larger number is divided by the smaller number, the quotient is 1 with a remainder of 16. What are the two numbers? I'm not even sure what

Question 284341: The sum of two numbers is 56.
If the larger number is divided by the smaller number, the quotient is 1 with a remainder of 16. What are the two numbers?
I'm not even sure what kind of algebra this falls into - or where to start.
Found 2 solutions by stanbon, richwmiller:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The sum of two numbers is 56.
If the larger number is divided by the smaller number, the quotient is 1 with a remainder of 16. What are the two numbers?
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Equations:
x + y = 56
x/y = 1 + 16/y
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Multiply thru the 2nd equation by "y":
------------------
x + y = 56
x = y + 16
------------------
Rearrange:
x + y = 56
x - y = 16
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Add and solve for "x":
2x = 72
x = 36
---
Substitute for "x" and solve for "y":
36 + y = 56
y = 20
==================
Cheers,
Stan H.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Start with what you are given.
The first sentences says the sum -- that means we are going to add
Then it says two numbers. We are dealing with algebra so we assign letters to those numbers. Let's use a and b
so we are adding
a+b
the sum is 56
is means equals
a+b=56
then it says the larger number. so far a and b are the same so we pick a for the larger number
a/b=1 + 16/b
[Explanation: this is not part of the problem : if you divide 5 by 3 and have a remainder of 2 what do you do with the 2 you put it over the 3 . let's do it with letters 5/x =1 plus remainder of 2 =1 2/x end of explanation]
back to the problem
so we have 16 remainder and put it over b
a/b=1 + 16/b
so now we have two equations with two unknowns
a+b=56
a/b=1 + 16/b
solve for a and b
a=36 b=20
check
a+b=56
36/20=1 16/20
ok
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