SOLUTION: Hi I am having problems completely solving this worded problem Five years ago Stephanie was four times as old as her daughter Kate. In 15 years, Stephanie will be five times as

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Question 1009815: Hi I am having problems completely solving this worded problem
Five years ago Stephanie was four times as old as her daughter Kate. In 15 years, Stephanie will be five times as old as Kate 2 years ago. Use simultaneous equations to determine Stephanie and Kate's current ages.
This is what I have worked out so far:
Stephanie= S, Kate= K
S-5= 4(K-5)
S= 4K-20+5
S= 4K-15 ... Equation 1
S+15= 5(K+15)
S= 5K+75-15
S= 5K+60 ... Equation 2
I think the next step is to substitute Equation 1 into 2:
4K-15= 5K+60
4K-5K= 60+15
-1K= 75 This is the point I get a bit stuck as if I divide both sides by
negative 1 the answer would be k= -75 which can't be correct as it
shouldn't be a negative number?
Any help would be much appreciated.
Found 2 solutions by josmiceli, josgarithmetic:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I think you missed part of the problem setup.
" In 15 years, Stephanie will be five times as old as Kate 2 years ago "
This would be:
+S+%2B+15+=+5%2A%28+K+-+2+%29+
+S+%2B+15+=+5K+-+10+
+S+=+5K+-+25+
------------------
You already have:
+S+=+4K+-+15+ ,so
+5K+-+25+=+4K+-+15+
+K+=+10+
and
+S+=+5K+-+25+
+S+=+5%2A10+-+25+
+S+=+50+-+25+
+S+=+25+
Kate is 10 and Stephanie is 25
Hope I got it

Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
Second sentence is less common but can be symbolized.

s and k for Stephanie and Kate; 


              Now         Five years ago        Fifteen years from now   Two years ago
Stepahnie     s           s-5                    s+15
Kate          k           k-5                    k+15                     k-2


Five years ago Stephanie was four times as old as her daughter Kate
s-5=4%28k-5%29
s-5=4k-20
s-4k=5-20
4k-s=15

In 15 years, Stephanie will be five times as old as Kate 2 years ago
s%2B15=5%28k-2%29
s%2B15=5k-10
s-5k=-15-10
5k-s=25

The described situation can be summarized with the system of equations,
system%284k-s=15%2C5k-s=25%29.
Solve the system for k and s.