Question

Patrick has P jellybeans. He has 1/3 (one third) as many jellybeans as Charles has. When combined, Patrick and Charles have 60 more jellybeans than Derek. In terms of P, how many jellybeans does Derek have?

a) P/3
b) P/2
c) P - 60
d) P + 60

Answer 1

In terms of P, Derek has P/3 jellybeans. Option A is answer.

Step-by-step explanation:

Let C be the number of jellybeans Charles has. Patrick has 1/3 as many, so P = C/3.

The total jellybeans for Patrick and Charles is P + C.

The combined total is 60 more than Derek's (D) jellybeans, so P + C = D + 60.

Substitute P = C/3 into the equation: C/3 + C = D + 60.

Find a common denominator, multiply both sides by 3 to clear the fraction:

C + 3C = 3D + 180.

Combine like terms:

4C = 3D + 180.

Express C in terms of P:

C = P/3.

Substitute into the equation: 4 * (P/3) = 3D + 180.

Solve for D:

D = P/3.

Therefore, Derek has Option A) P/3 jellybeans is answer.