Oliver has 3 times as many rocks in his collection as Katie. Then Oliver collected 75 more rocks and Katie collected 105 more rocks. Now Katie has the same number of rocks as Oliver. How many rocks did Oliver have at first?

Answer:Olivier had 45 rocks initially.

Step-by-step explanation:

Let x represent the number of rocks that Katie had initially.

Oliver has 3 times as many rocks in his collection as Katie. This means that Olivier originally had 3x rocks.

Then Oliver collected 75 more rocks and Katie collected 105 more rocks. This means that Olivier now has 3x + 75

Also, Katie now has x + 105

Now Katie has the same number of rocks as Oliver. It means that

3x + 75 = x + 105

3x - x = 105 - 75

2x = 30

x = 30/2 = 15

Therefore, the number of rocks that Olivier had initially is

15 * 3 = 45

The answer to your question is Katie had 15 rocks and Oliver 45 rocks.

Step-by-step explanation:

Conditions

Katie has x amount of rocks

Oliver has 3x amount of rocks

The final amount of rocks

Oliver = 3x + 75

Katie = x + 105

Now, they have the same amount of rocks, then we can equal both equations

3x + 75 = x + 105

Solve for x

3x - x = 105 - 75

2x = 30

x = 30/2

x = 15

Conclusions

At first Katie had 15 rocks and Oliver had 3 (15) = 45 rocks