Final answer:
The student is asked to solve an algebraic equation representing a word problem. We first set up the equation according to the given conditions, and then solve for x through cross-multiplication and algebraic manipulation to find that the number in question is 26.
Step-by-step explanation:
Let's define the variable x as the number we want to find. According to the problem, if twice a number added to 3 is divided by the number plus 7, the result is five-thirds. Mathematically, this can be expressed as the equation
(2x + 3) / (x + 7) = 5/3.
To solve this equation, we can cross-multiply to eliminate the fraction:
3(2x + 3) = 5(x + 7)
Now we distribute on both sides:
6x + 9 = 5x + 35
Subtract 5x from both sides to get:
x + 9 = 35
Then subtract 9 from both sides to solve for x:
x = 26
The number we were looking for is 26.