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if the larger of two integers whose sum is 85 is divided by the smaller, the quotient is 7 and the remainder is 5. what are the two numbers?

Sagot :

If the larger(x) of two integers(x and y) whose sum is 85,
     x+y=85 or x=85-y
is divided by the smaller(y),
     *the larger(x) divided by the smaller(y)
                     x
                     -
                     y
the quotients is 7 and the remainder is 5.
                     x
                     -    =   7+5/y
                     y
     *substitute x=85-y
(85-y)
--------   =  7+5/y
    y
     *to remove the denominators(y), multiply (y) on both sides
(85-y)
--------   (y) =  7(y)+5/y (y)
    y
85-y=7y+5
-5+85=7y+y
80=8y
---------
    8
y=10
     *now that you have (y=10) substitute (y) to the first equation,
x+y=85
x+(10)=85
x=85-10
x=75
What are the two numbers?
x=75    &     y=10