Hi Roseland,
The first thing we can notice from this question is that we need two variables to write our system of equations(Ruth's age and the son's age).; this also means that we need two equations!
Current Day:
let R=Ruth's Age
let s= Ruth's son Age
R=s+22
Seven Years Ago:
let R-7 = Ruth's age 7 years ago
let s-7 = Ruth's son age 7 years ago
R-7= 3(s-7)
There are our two equations, let's write them write under each other so that it looks pretty...
R=s+22
R-7=3(s-7)
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Now our job is to solve these 2 equations:
If you recall, we can use either the "substitution method" or the "addition method" to solve simultaneous equations.
First we are going to solve for s in the first equations... subtract 22 on both sides to yield
s=R-22
Now we can plug this value of s into our second equation:
R-7 = 3(R-22-7)
since we only have R's now, we can solve for R...
By distributing the 3 we get:
R-7 = 3R-66-21
combining terms...
R-7 = 3R - 87
continuing on...
-2R = -80
diving by -2...
R = 40
substituting R=40 into our earlier equation R= s+22
40 = s + 22
s= 18.
Now we know how old each person is...
Currently, Ruth is 40 and her son is 18
Seven years ago, Ruth was 33 and her son was 11
I hope this helps... Merry Christmas!
