This question is confusing me

She went on the slide 8 times and on the roller coaster 4 times

Step-by-step explanation:

We convert each statements to a mathematical equation.

Firstly, let's represent the number of times she went on the coaster with R and the number of times on the slide with S. We know quite well she went on 12 rides. Hence the summation of both number of times yield 12.

Mathematically, R + S = 12. (i)

Now we also know her total wait time was 3hours. Since an hour equals 60 minutes, her total wait time would equal 180 minutes.

To get a mathematical representation for the wait time, we multiply the number of roller coaster rides by 25 and that of the slides by 10.

Mathematically, 25R + 10S = 180 (ii)

Here we now have two equations that we can solve simultaneously.

From equation 1 we can say R = 12 - S. We can then substitute this into equation 2 to yield the following:

25(12 - s) + 10s = 180

300 - 25s + 10s = 180

300 - 25s + 10s = 180

300 - 15s = 180

15s = 300 - 180

15s = 120

S = 120/15

S = 8

S = 8 , and R = 12 - S = 12 - 8 = 4

The first multiple of 12 after 38 is 48.

The first multiple of 12 before 316 is 312.

So we have, 48, 60, 72... 312.

Divide by 12...

4, 5, 6, ... 26

Subtract 3 from each term to get... 1, 2, 3... 23

So there are 23 terms!

Hope this helps!