Rose was buying fruit at the local market to make a fruit cake for Christmas. The recipe calls for plums, apples, and oranges. She needed 3 more oranges than plums and three times as many apples than plums. If she bought 28 pieces of fruit, how many oranges did she buy?

O = P+3

A = 3P

O + A + P = 28

substituting ... (P+3) + 3P + P = 28

To solve this problem, let's assign variables to the quantities mentioned:

Let's say:
P = number of plums
A = number of apples
O = number of oranges

According to the problem, Rose needed 3 more oranges than plums, so we can write the equation:
O = P + 3

The problem also states that she needed three times as many apples as plums:
A = 3P

We know that she bought a total of 28 pieces of fruit, so we can write another equation:
P + A + O = 28

Now we have a system of equations:
O = P + 3
A = 3P
P + A + O = 28

To solve the system, we can substitute the second equation into the third equation:
P + (3P) + (P + 3) = 28
5P + 3 = 28
5P = 25
P = 5

Now we can substitute the value of P into the first equation to find O:
O = 5 + 3
O = 8

Therefore, Rose bought 8 oranges.