# In the 30 day month of April, for every three days it rained, there were two days it did not rain. The number of days in April on which it rained was how much greater than the number of days on which it did not rain?

## days rained : days not rained = 3:2 = 3x : 2x

3x + 2x = 30

5x = 30

x = 6

number of days it rained = 18, number it did not rain = 12

what is the difference in those two results?

## Well, April showers bring May flowers, but it seems like April didn't want to stick to the script! So, let's do some math and clown around with this puzzle.

If for every three rainy days, we have two non-rainy days, we can create groups of five days. Within each group, we have three rainy days and two non-rainy days.

Now, let's see how many groups of five days fit into April. Since April has 30 days, we can divide it by 5:

30 / 5 = 6

So, we have six groups of five days in April. In each group, we have three rainy days and two non-rainy days. Therefore, in total, we had:

6 groups * 3 rainy days = 18 rainy days

6 groups * 2 non-rainy days = 12 non-rainy days

Therefore, the number of days in April on which it rained is 18 - 12 = 6 days greater than the number of days on which it did not rain. It seems like April had a rainy sense of humor!

## To solve this problem, let's break down the information given step-by-step.

Step 1: Determine the ratio of rainy days to non-rainy days in April.

According to the information given, for every three days it rained, there were two days it did not rain. This can be represented as a ratio: 3:2. This means that out of every 5 days (3 + 2), it rained for 3 days and did not rain for 2 days.

Step 2: Calculate the number of times the 5-day cycle occurs in April.

Since April is a 30-day month, we need to find out how many times the 5-day cycle occurs within it. To do this, we divide 30 (the total number of days in April) by 5 (the length of the cycle).

30 ÷ 5 = 6

This means that the 5-day cycle of rainy days and non-rainy days repeats 6 times in April.

Step 3: Calculate the number of rainy days and non-rainy days in April.

Now that we know the number of times the 5-day cycle repeats in April (6 times), we can calculate the number of rainy and non-rainy days.

In each cycle, there are 3 rainy days and 2 non-rainy days.

Number of rainy days = 3 rainy days/cycle × 6 cycles = 18 rainy days

Number of non-rainy days = 2 non-rainy days/cycle × 6 cycles = 12 non-rainy days

Step 4: Calculate the difference between the number of rainy days and non-rainy days.

To find the difference between the number of rainy and non-rainy days, we subtract the number of non-rainy days from the number of rainy days.

Difference = Number of rainy days - Number of non-rainy days

Difference = 18 rainy days - 12 non-rainy days

Difference = 6

Therefore, the number of days in April on which it rained is 6 days greater than the number of days on which it did not rain.

## To find the number of days in April on which it rained, we can set up a ratio based on the information given.

We know that for every three days it rained, there were two days it did not rain. Let's call the number of days it rained "x" and the number of days it did not rain "y".

Based on the ratio, we can set up the equation:

(x / y) = (3 / 2)

To solve for x, we can cross multiply:

2x = 3y

Divide both sides by 2:

x = (3y / 2)

Since x represents the number of days it rained and y represents the number of days it did not rain, we now need to find a pair of numbers that satisfy this equation.

Since April is a 30-day month, we can substitute y with 30 - x. This is because the total number of days in April is equal to the sum of days it rained and days it did not rain.

Substituting y with 30 - x in the equation, we have:

x = (3(30 - x) / 2)

Now, we can solve this equation to find the value of x.

Expanding the equation, we get:

2x = 90 - 3x

Combining like terms:

5x = 90

Divide both sides by 5:

x = 18

Therefore, the number of days in April on which it rained is 18.

To find the number of days on which it did not rain, we can substitute this value back into the equation:

y = 30 - x

y = 30 - 18

y = 12

So, the number of days in April on which it rained is 18, which is 6 days greater than the number of days on which it did not rain (12).