SOLUTION: A is eleven times as old as B. In a certain number of years A will be five times as old as B, and five years after that she will be three times as old as B. How old are they now?

Question 402002: A is eleven times as old as B. In a certain number of years A will be five times as old as B, and five years after that she will be three times as old as B. How old are they now?
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A is eleven times as old as B. In a certain number of years A will be five times as old as B, and five years after that she will be three times as old as B. How old are they now?
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Equations:
a = 11b
(a+x)= 5(b+x)
(a+x+5) = 3(b+x+5)
----------------------
Substitute for "a":
11b+x = 5b+5x
11b+x+5 = 3b+3x+15
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Rearrange:
6b - 4x = 0
8b - 2x = 10
------
Divide thru the 1st equation by 2 to get:
3b - 2x = 0
8b - 2x = 10
---
Subtract 1st from 2nd and solve for "b":
5b = 10
b = 2 yrs old
---
Solve for "a":
a = 11b
a = 22 yrs old
----
Cheers,
Stan H.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write an equation for each statement, simplify each equation:
:
"A is eleven times as old as B."
a = 11b
:
"In a certain number of years A will be five times as old as B,"; y = no. of yrs
a + y = 5(b+y)
a + y = 5b + 5y
a = 5b + 5y - y
a = 5b + 4y
replace a with 11b
11b = 5b + 4y
11b - 5b = 4y
6b = 4y
6b - 4y = 0
:
"five years after that she will be three times as old as B." That's y+5 yrs
a + y + 5 = 3(b + y + 5)
a + y + 5 = 3b + 3y + 15
a = 3b + 3y - y + 15 - 5
a = 3b + 2y + 10
replace a with 11b
11b = 3b + 2y + 10
11b - 3b = 2y + 10
8b = 2y + 10
8b - 2y = 10
:
Multiply above equation by -2, add to the 1st equation
-16b + 4y = -20
6b - 4y = 0
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-10b = -20
b = 2 yrs old
Find a
a = 11(2)
a = 22 yrs old
:
We can say their present ages are: A=22; B=2
:
:
To check our our solutions, Find y
6(2) - 4y = 0
12 - 4y = 0
-4y = -12
y = 3 yrs is that "certain number of years"
;
Check in the statement:
"In a certain number of years A will be five times as old as B,
22 + 3 = 5(2 + 3)
25 = 25
:
You can check the solutions in the 3rd statement:
"five years after that she will be three times as old as B." That's y+5 yrs"

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