If Angel plants the same number of flowers in each of 5 rows, he will have none left over. If he plants 1 in the first row and then 1 more in each row than he did in the previous row, he will plant flowers in only 4 rows. how many flowers does he have?
The number of flowers is evenly divisible by 5.
Planting 1,2,3, and 4 in four rows, with none left over, uses up 10 plants.
The number 10 meets both requirements
10
Let's find the total number of flowers Angel has.
The first scenario states that Angel plants the same number of flowers in each of 5 rows, and he has none left over. In this case, we can assume that he plants x flowers in each row. Therefore, the total number of flowers will be 5x.
Now, in the second scenario, Angel plants 1 flower in the first row and then 1 more in each subsequent row than he did in the previous row, for only 4 rows. This means that he plants 1 flower in the first row, 2 flowers in the second row, 3 flowers in the third row, and 4 flowers in the fourth row. From this, we can see that the total number of flowers in the second scenario is 1 + 2 + 3 + 4 = 10.
Since the total number of flowers must be the same in both scenarios, we have:
5x = 10
Now, let's solve for x by dividing both sides of the equation by 5:
x = 10/5
x = 2
Therefore, Angel has 2 flowers in each row, and since there are 5 rows in total, he has a total of 5 * 2 = 10 flowers.
To determine the total number of flowers Angel has, we need to find the number of flowers in each row and then sum them up.
In the first case, where Angel plants the same number of flowers in each of 5 rows and has none left over, we can assume that he plants x flowers in each row. Therefore,
Total number of flowers = x + x + x + x + x = 5x
In the second case, where Angel plants 1 flower in the first row and then 1 more in each subsequent row to only reach 4 rows, we can assume that he plants x flowers in the first row. Therefore,
Total number of flowers = x + (x+1) + (x+2) + (x+3) = 4x + 6
Since the total number of flowers must be the same in both cases, we can equate the two expressions:
5x = 4x + 6
To solve this equation, we subtract 4x from both sides:
5x - 4x = 6
x = 6
Substituting this value back into the expressions, we can find the total number of flowers:
Total number of flowers = 5(6) = 30
Therefore, Angel has 30 flowers.