Final answer:
To find out how much Bob earns, we can set up an equation using the given information and solve for x. After solving the equation, we find that Bob earns $120.
Step-by-step explanation:
To solve this problem, we can start by assuming that Bob's earnings are represented by the variable x. According to the given information, Bob spent (1/2) of his earnings on a pair of shorts. This means that he spent (1/2) * x = x/2 on shorts. After that, he spent (1/2) of what remained on a present, which is (1/2) * (x - x/2) = (1/2) * (x/2) = x/4 on the present. The total amount spent is given as $90, so we can set up the equation x/2 + x/4 = 90 and solve for x.
Combining like terms, we have (2x + x)/4 = 90. Simplifying further, we get 3x/4 = 90. To isolate x, we can multiply both sides of the equation by 4/3, resulting in x = 90 * 4/3 = 120.
Therefore, Bob earns $120.