The product of positive numbers is 48. The larger number is 13 more than the smaller. What are both numbers?

1 Answer
Mar 13, 2018

Larger number: #16#
Smaller number #3#

Explanation:

Suppose the larger number is #a# and the smaller number is #b#.
You solve the following system of equations:
#a*b=48#
#a-13=b#

Since #b# is #a-13#, you can plug that into #a*b=48#, so...
#a*(a-13)=48#
#a^2-13a=48#
#a^2-13a-48=0#

Factor the polynomial:
#(a-16)(a+3)=0#
#a=16 or a=-3#

#a# is positive so #a=16#.

We can now solve for #b# by plugging in #a#, so...
#16-13=b#
#3=b#

We have #a=16# and #b=3#, meaning that
the larger number is #16# and the smaller number is #3#.