The product of two integers is 150. One integer is 5 less than twice the other. How do you find the integers?

1 Answer
Alan P.
Jul 27, 2016

The integers are #color(green)(10)# and #color(green)(15)#

Explanation:

Let the integers be #a# and #b#
We are told:
#color(white)("XXX")a * b =150#
#color(white)("XXX")a=2b-5#

Therefore
#color(white)("XXX")(2b-5) * b =150#

After simplifying
#color(white)("XXX")2b^2-5b-150=0#

Factoring
#color(white)("XXX")(2b+15)*(b-10)=0#

#{:(2b+15=0," or ",b-10=0),(rarrb=15/2,,rarr b=10),("impossible",,),("since b integer",,):}#

So #b=10# and since #a=2b-5 rarr a=15#

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