Question 1191620: james is 4 years less than 7 times the age of his daughter,who is 4 more than half of her brothers age. the sum of their ages is 38. How old is James?
Found 3 solutions by josgarithmetic, MathTherapy, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
james is 4 years less than 7 times the age of his daughter,who is 4 more than half of her brothers age. the sum of their ages is 38. How old is James?
Let daughter's age be D
Then James' age is 7D - 4
Also, daughter's age, or 
Since all ages sum to 38, we get: D + 7D - 4 + 2D - 8 = 38
10D - 12 = 38
18D = 50
Daughter's age, or 
James' age: 7(5) - 4 = 35 - 4 = 31
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
There are always many different ways to go about setting up a problem like this for solving with formal algebra.
I am a big advocate of looking ahead at the relationship between the numbers to find a way to set the problem up that leads to the simplest calculations.
Since the daughter's age is 4 more than half her brother's age, I would start the problem by defining the brother's age as 2x, so that the expression for "4 more than half the brother's age" does not involve fractions. Doing that, we get
2x = brother's age
x+4 = daughter's age (4 more than half her brother's age)
7(x+4)-4 = James's age (4 less than 7 times his daughter's age)
This is exactly the setup used by tutor @josgarithmetic, leading to a solution with simple calculations.
(2x)+(x+4)+(7(x+4)-4) = 38
10x+28 = 38
10x = 10
x = 1
ANSWER: James's age is 7(1+4)-4 = 35-4 = 31
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