First, let's call Stephanie's age ss and Matthews age mm:
Now, we can write the two sentences in terms of a math equation:
s = 3m - 4s=3m−4
s*m = 260s⋅m=260
Now, because the first equation is already in terms of ss we can substitute 3m - 43m−4 into the second equation for ss and solve for mm:
(3m - 4)m = 260(3m−4)m=260
3m^2 - 4m = 2603m2−4m=260
3m^2 - 4m - 260 = 260 - 2603m2−4m−260=260−260
3m^2 - 4m - 260 = 03m2−4m−260=0
(3m + 26)(m - 10) = 0(3m+26)(m−10)=0
Now we can solve each term for 00:
3m + 26 = 03m+26=0
3m + 26 - 26 = 0 - 263m+26−26=0−26
3m = -263m=−26
(3m)/3 = -26/33m3=−263
m = -26/3m=−263
and
m - 10 = 0m−10=0
m - 10 + 10 = 0 + 10m−10+10=0+10
m = 10m=10
Because age cannot be negative we will use 1010 to substitute for mm in the first equation and calculate ss:
s = 3*10 - 4s=3⋅10−4
s = 30 - 4s=30−4
s = 26s=26
