The sum of two integers is #56#. If we subtract #6# from each of the integers, the larger answer divided by the smaller is #43#. What are the two integers?

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Answer 1 · 2017-07-27T22:33:59

The solution is that the two integers are 7 and 49.

Let's call the larger integer 'm' and the smaller one 'n'.

We have Equation 1:

#m+n=56#

And Equation 2:

#(m-6)/(n-6)=43#

Let's do a little work on Equation 2:

#m-6=43(n-6)=43n-258#

#m=43n-252#

We can substitute this value for #m# into Equation 1:

#43n-252+n=56#

#44n-252=56#

#44n=308#

#n=7#

Going back to Equation 1:

#m+7=56#

#m=49#