SOLUTION: sue is now seven times old as louise. in six years sue will be five time as old as louise. find the present age of each one.

Question 201720: sue is now seven times old as louise. in six years sue will be five time as old as louise. find the present age of each one.
Found 3 solutions by stanbon, Earlsdon, Theo:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
sue is now seven times as old as louise. in six years sue will be five time as old as louise. find the present age of each one.
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NOW DATA:
Let louise be x yrs. old
Then sue is 7x yrs. old
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Six years from now DATA:
louise will be x+6 yrs. old
sue will be 7x+6 yrs. old
-----------------------------------
Equation based on 6 yrs from now data:
sue = 5(louise)
7x+6 = 5(x+6)
7x+6 = 5x+30
2x = 24
x = 12 (louise's age NOW)
7x = 84(sue's age NOW)
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Cheers,
Stan H.

Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Let L = Louise' present age and S = Sue's present age.
1) S = 7*L "Sue is now seven times as old as Louise."
2) S+6 = 5(L+6) "In six years Sue will be five times as old as Louise (will be in six years)"
Substitute S = 7*L from equation 1) into equation 2) and solve for L.
2a) 7*L+6 = 5(L+6) Simplify.
2a) 7L+6 = 5L+30 Subtract 5L from both sides.
2a) 2L+6 = 30 Subtract 6 from both sides.
2a) 2L = 24 Divide both sides by 2
2a) L = 12 and S = 7*L = 7*12 = 84
Louise is 12 years old and Sue is 84 years old.
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
sue is now 7 times as old as louise.
let x = sue's age now.
let y = louise's age now.
x = 7 * y
in 6 years sue will be x + 6 years old.
in 6 years louise will be y + 6 years old.
in 6 years sue will be 5 times as old as louise.
x + 6 = 5 * (y + 6)
simplify to get
x + 6 = 5*y + 30
subtract 6 from both sides of the equation and subtract 5*y from both sides of the equation to get
x - 5*y = 30 - 6
which becomes
x - 5y = 24
since x = 7y (from above) we get
7y - 5y = 24
simplify to get
2y = 24
divide both sides by 2 to get
y = 12
since y is louise's age now, then louise is 12 years old now.
since sue is 7 times as old as louise now, then sue is 84.
in 6 years from now sue will be 90 and louise will be 18.
sue will be 5 times as old as louise.
everything checks out.
x = sue's age now = 84
y = louise's age now = 12.

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