Question 1203623
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You have received two good formal algebraic solutions, one using two variables and the other using one.  I myself nearly always find using a single variable is easier... but it is a personal choice for each student.<br>
If formal algebra is not required, a quick mental solution can be good problem-solving exercise.<br>
The sum of their ages is 53, and one of them is 7 years older than the other.<br>
So subtract 7 from the age of the older person; that subtracts 7 from the sum of their ages.<br>
That leaves you with two people with the same age, and the sum of their ages is 63-7 = 56; so each of them is 56/2 = 28 years old.<br>
Now add the 7 years back on to the older person's age to find the two ages are 28 and 28+7 = 35.<br>
ANSWER: Jack (the older) is 35 years old<br>