Question 1150559: If you add Natalie's age and Fred's age, the result is 38. If you add Fred's age to 4 times Natalie's age, the result is 74. Write and solve a system of equations to find how old Fred and Natalie are.
Found 2 solutions by jim_thompson5910, greenestamps:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
N = Natalie's age
F = Fred's age
both ages are in years, and they are current present day ages
"If you add Natalie's age and Fred's age, the result is 38." means the first equation is F+N = 38.
Solve for F to get F = 38 - N. You subtract N from both sides. We'll use this equation later.
"If you add Fred's age to 4 times Natalie's age, the result is 74." so the second equation is
F + 4*N = 74
Now plug in F = 38 - N. Solve for N.
F + 4*N = 74
38 - N + 4*N = 74 ... replaced F with 38-N
38 + 3N = 74
38 + 3N-38 = 74-38 .... subtracting 38 from both sides
3N = 36
3N/3 = 36/3 .... divide both sides by 3
N = 12
Use this to find Fred's age
F = 38 - N
F = 38 - 12 ... plug in N = 12
F = 26
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To summarize, the system of equations is
F + N = 38
F + 4N = 74
Solving said system leads to N = 12 and F = 26. This means Natalie is 12 years old and Fred is 26 years old.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The two equations, as shown by the other tutor, are indeed
F+N = 38
F+4N = 74
But with the two equations in that form, using substitution is the long way around; the two equations are perfectly suited for solving by elimination.
Subtracting the first equation from the second yields
3N = 36
which immediately gives us
N = 12
and then the first equation gives us
F = 26
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