SOLUTION: Good evening, I have an age application problem that I need assistance with. I will greatly appreciate your help. If Leah is 6 years older than Sue, and John is 5 years older than

Question 545043: Good evening, I have an age application problem that I need assistance with. I will greatly appreciate your help. If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages are 41, then how old is sue? What I have done so far with this problem: L+S+J=41
L(6+s)+S+J(5+L)=41
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Your first equation is correct. That is:
.
L + S + J = 41
.
You are told that Leah is 6 years older than Sue. This means if you add 6 years to Sue's age, the sum will equal Leah's age. So you can say:
.
L = S + 6
.
Now you can return to your first equation and substitute S + 6 for its equal, which is L. When you make that substitution the first equation becomes:
.
S + 6 + S + J = 41
.
Simplify this by adding the two S terms. Then subtract 6 from both sides to get rid of the 6 on the left side. These two simplifications make the equation become:
.
2S + J = 35
.
You are also told that John is 5 years older than Leah. This means that if you add 5 years to Leah's age, the sum will equal John's age. So you can say:
.
J = L + 5
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But you know that L = S + 6. So in this equation for J, you can substitute S + 6 for L to get:
.
J = S + 6 + 5
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and by adding 6 + 5, you make the equation:
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J = S + 11
.
Return to the equation 2S + J = 35 and substitute S + 11 for J to get:
.
2S + S + 11 = 35
.
Combine the 2 terms containing S and then subtract 11 from both sides to get rid of the 11 on the left side. These two simplifications make the equation become:
.
3S = 24
.
Solve for S by dividing both sides of this equation by 3 to get that S (Sue's age) is:
.
S = 24/3 = 8
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Sue is 8 years old.
.
That means that Leah's age (she's 6 years older than Sue) is 8 + 6 = 14. And John is 5 years older than Leah so John is 14 + 5 = 19. Just as a check, let's add these three ages to see if the total is 41 as it should be:
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8 + 14 + 19 = 22 + 19 = 41
.
That is correct.
.
So you can have confidence that Sue is 8 years old and that is the answer that the problem asked you to find.
.
Hope this helps you to understand how the problem can be solved. You were very close with your second equation, but you had to find L and J in terms of S to get to the answer.
.
Your second equation should have been:
.

.
Note that you could have substituted 6 + S for L in one more place. Then it would have worked out for you because your equation would be:
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(6 + S) + S + 5 + (6 + S) = 41
.
And combining the S terms would simplify this equation to:
.
3S + 6 + 5 + 6 = 41
.
and combining the constants on the left side would give:
.
3S + 17 = 41
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Subtracting 17 from both sides:
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3S = 24
.
and by dividing both sides by 3 again results in:
.
S = 24/3 = 8
.
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