Question 472729: 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 monika_p, Theo:
Answer by monika_p(71)   (Show Source):
You can put this solution on YOUR website! a-Henry's age
b-Daisy's age
From information you have you can write 2 equations
1/2a+1/3b=11
(a+6)+(b+6)=40
Solve it as system of 2 equations
from second equation find a
a=40-12-b
a= 28-b
put it in first equation and find b
1/2(28-b)+1/3b=11
14-1/2b+1/3b=11
-3/6b+2/6b=-3
-1/6b=-3
b=18 then a= 28-18=10
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! let x = henry's age.
let y = daisy's age.
half of henry's age added to 1/3 of daisy's age is equal to 11.
in equation form, this becomes:
x/2 + y/3 = 11
6 years from now the sum of their ages will be 40.
in equation form, this becomes:
(x+6) + (y+6) = 40
if we multiply the first equation by 6, then we get:
3x + 2y = 66
that removes the fractions from the first equation.
if we simplify the second equation by combining like terms, we get:
x + y + 12 = 40
if we subtract 12 from both sides of this equation, we get:
x + y = 28
solving for y, we get:
y = 28 - x
we replace y with 28 - x in the first equation to get:
3x + 2y = 66 becomes:
3x + 2 * (28-x) = 66
now we have one equation in one unknown which we can solve for.
simplify this equation to get:
3x + 56 - 2x = 66
combine like terms to get:
x + 56 = 66
subtract 56 from both sides of this equation to get:
x = 10
substitute for x in the equation of x + y = 28 to get:
y = 28 - x which becomes:
y = 28 - 10 which becomes:
y = 18
we have x = 10 and y = 18
this means:
henry's age is 10
daisy's age is 18
half of henry's age added to 1/3 of daisy's age is equal to 11.
half of henry's age is 5.
one third of daisy's age is 6
5 + 6 = 11
so far so good.
6 years from now the sum of their ages will be 40.
6 years from now, henry is 16.
6 years from now, daisy is 24.
16 + 24 = 40.
both requirements of the problem are solved, so the solutions are good.
henry is 10 years old.
daisy is 18 years old.
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