SOLUTION: Find two numbers whose sum is 163 such that when the larger number is divided by the smaller, the quotient is 3 and the remainder is 3.

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Question 669208: Find two numbers whose sum is 163 such that when the larger number is divided by the smaller, the quotient is 3 and the remainder is 3.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
a = the larger integer
b = the smaller integer
Their sum is 163 translates into a%2Bb=163
When the larger number is divided by the smaller, the quotient is 3 and the remainder is 3 translates into
a=3b%2B3 (If you need it, see the explanation below).

You end up with the system
system%28a%2Bb=163%2Ca=3b%2B3%29
which can be easily solved by substitution.
Substituting a=3b%2B3 into a%2Bb=163 you get
3b%2B3%2Bb=163 <--> 4b%2B3=163 <--> 4b=163-3 <--> 4b=160 <--> 4b%2F4=160%2F4 <--> highlight%28b=40%29
Then, substituting b=40 into a=3b%2B3 we get
a=3%2A40%2B3 <--> a=120%2B3 <--> highlight%28a=123%29

EXPLANATION OF WHAT DIVISION, QUOTIENT, AND REMAINDER MEAN:
The quotient is 3.
That means that b fits up to 3 times (but not 4 times) into a,
so that 3b is no larger than a (3b%3C=a),
but 4b does not fit into a.
It is larger, 4b%3Ea
There is a remainder. It is 3.
It turns out that 3b%3Ca and the difference is the remainder
a-3b=3 <--> a=3b%2B3