Ikelyn thinks you've already finished the section on 3 equations in 3 unknowns,
and that now you are studying clever ways of getting answers without using the
methods of solving 3 equations in 3 unknowns. Or --
She might be trying to show us how smart she is (or how dumb I am for not using
her "clever" method).
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Anyway,
Instead of doing your homework for you, I'll do one exactly like yours
but change all the numbers: I'll do this one:
There are three boys, Cyril, Ryan, and Guye. The sum of their ages
is sixty years. Cyril’s age added to Guye’s is five times Ryan’s age,
and Ryan’s age added to Cyril’s is five times Guye’s. How old are
the three boys?
The sum of their ages is sixty years.
C + R + G = 60
Cyril’s age added to Guye’s is five times Ryan’s age,
G+C = 5R
and Ryan’s age added to Cyril’s is five times Guye’s.
C + R = 5G
Get the terms in order and lined up vertically
Eliminate C and G by multiplying the first equation by -1
and adding the second equation to it:
-C - R - G = -60
C - 5R + G = 0
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0 -6R + 0 = -60
-6R = -60
R = 10
Substitute 10 for R in all three equations:
Simplify
Simplify further:
The first two equations are the same so eliminate one of them:
Solve the first equation for C
C = 50 - G
Substitute (50 - G) for C in the second equation:
50 - G - 5G = -10
50 - 6G = -10
-6G = -60
G = 10
Substitute 10 for R and 10 for G in
C + R + G = 60
C + 10 + 10 = 60
C + 20 = 60
C = 40 <--Cyril is a 40-year-old "BOY". lol
Now do yours the same way. Cyril will be a BOY in your problem. lol
Edwin