Question 1191620
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There are always many different ways to go about setting up a problem like this for solving with formal algebra.<br>
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.<br>
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<br>
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)<br>
This is exactly the setup used by tutor @josgarithmetic, leading to a solution with simple calculations.<br>
(2x)+(x+4)+(7(x+4)-4) = 38
10x+28 = 38
10x = 10
x = 1<br>
ANSWER: James's age is 7(1+4)-4 = 35-4 = 31<br>