Question 206804: Half of Henry's age added to 1/3 of Daisy's age is 11 years. Six years from now the sum of their ages will be 40 years how old is each? Found 2 solutions by ankor@dixie-net.com, profemmanuel2q@yahoo.com:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Let h = Henry's present age
Let d = Daisy's present age
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Just write an equation for what it says:
"Half of Henry's age added to 1/3 of Daisy's age is 11 years." h + d = 11
Multiply by 6 to get rid of the fractions, results:
3h + 2d = 66
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" Six years from now the sum of their ages will be 40 years"
(h+6) + (d+6) = 40
h + d + 12 = 40
h + d = 40 - 12
h + d = 28
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how old is each?
Multiply the above equation by 2 and subtract from the 1st equation
3h + 2d = 66
2h + 2d = 56
---------------subtraction eliminates d, find h
h = 10
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I'll let you find d, then check the two solutions in both equations
You can put this solution on YOUR website! Half of Henry's age added to 1/3 of Daisy's age is 11 years. Six years from now the sum of their ages will be 40 years how old is each?
Let Henry's age be x and Daisy's age be y
Half of Henry's age added to 1/3 of Daisy's age is 11 years can be expressed as 1/2x + 1/3y = 11 ---- Eqn 1 Multiply eQN - 1 both 6 to cancel the denominator
3x + 2y = 66 ---- 1
Six years from now the sum of their ages will be 40 years
Henry will be (x + 6) and Daisy will (y + 6), Their sum will be x + 6 + y + 6 = 40
x + y = 40 - 6 - 6
x + y = 28 --- Eqn 2
Joining Eqn 1 and Eqn. 2
3x + 2y = 66 ---- 1
x + y = 28 --- Eqn 2
Multiply Eqn 2 by 2
3x + 2y = 66 ---- 1
2x + 2y = 56 ---- 2
Eqn 1 - Eqn 2
x = 10
Put x = 10 into Eqn. 1
3(10) + 2y = 66
30 + 2y = 66
2y = 66 - 30
2y = 36
Divide both sides by 2
y = 18
Hence, Henry is 10 years and Daisy is 18 years
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