Stephanie s age is 4 years less than 3 times Matthew's age. If the product of their ages is 260, how old is Stephanie?

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Answer 1 · 2016-12-07T14:19:25

Stephanie is 26.

First, let's call Stephanie's age #s# and Matthews age #m#:

Now, we can write the two sentences in terms of a math equation:

#s = 3m - 4#

#s*m = 260#

Now, because the first equation is already in terms of #s# we can substitute #3m - 4# into the second equation for #s# and solve for #m#:

#(3m - 4)m = 260#

#3m^2 - 4m = 260#

#3m^2 - 4m - 260 = 260 - 260#

#3m^2 - 4m - 260 = 0#

#(3m + 26)(m - 10) = 0#

Now we can solve each term for #0#:

#3m + 26 = 0#

#3m + 26 - 26 = 0 - 26#

#3m = -26#

#(3m)/3 = -26/3#

#m = -26/3#

and

#m - 10 = 0#

#m - 10 + 10 = 0 + 10#

#m = 10#

Because age cannot be negative we will use #10# to substitute for #m# in the first equation and calculate #s#:

#s = 3*10 - 4#

#s = 30 - 4#

#s = 26#