Final answer:
By using algebra to establish relationships between the amounts Diane, Carlos, and Abdul have in their wallets, it's determined that Diane has $9, which doesn't match any of the given options. Carlos has $16, and Abdul has $64. The algebraic expressions used account correctly for the total of $89.
Step-by-step explanation:
To solve the problem, we need to use algebra to set up equations based on the given information. Let's denote the amount of money Diane has as D, Carlos as C, and Abdul as A. We know that Carlos has $7 more than Diane, so C = D + 7. Abdul has 4 times what Carlos has, thus A = 4C. Together, they have $89, so the equation is D + C + A = 89. Substituting the relationships into the equation, we get D + (D + 7) + 4(D + 7) = 89.
Simplifying, we get 6D + 35 = 89. Subtracting 35 from both sides, we have 6D = 89 - 35, which equals 6D = 54. Dividing both sides by 6, we find out that D = 9. Therefore, Diane has $9, Carlos has $9 + $7 = $16, and Abdul has 4 times what Carlos has so, A = 4 \times 16 = $64. Together, 9 + 16 + 64 = $89, confirming that the amounts are correct. Unfortunately, the options provided for Diane's wallet do not match the calculated amount.