Question

each plant in Johns garden has either 5 leaves or 2 leaves and 1 flower. In total, tge plants hace 6 flowers and 32 leaves. How many plants are there?

Answer 1

Let's use a system of equations to solve this problem:Let x be the number of plants with 5 leaves.

Let y be the number of plants with 2 leaves and 1 flower.From the problem, we know that:Each plant has either 5 leaves or 2 leaves and 1 flower, so the total number of plants is x + y.There are 6 flowers in total, so the number of plants with 2 leaves and 1 flower is y = 6.There are 32 leaves in total, so the total number of leaves from plants with 5 leaves is 5x, and the total number of leaves from plants with 2 leaves and 1 flower is 2y = 12.Putting it all together:x + y = total number of plants

y = 6

5x + 2y = 32Substituting y = 6 in the third equation:

5x + 2(6) = 32

5x + 12 = 32

5x = 20

x = 4So there are 4 plants with 5 leaves, and 6 plants with 2 leaves and 1 flower, for a total of x + y = 4 + 6 = 10 plants.

Answer 2

Let's call the number of plants with 5 leaves as "x" and the number of plants with 2 leaves and 1 flower as "y".

From the problem statement, we know that:

Each plant with 5 leaves has no flowers.

Each plant with 2 leaves and 1 flower has 2 leaves and 1 flower.

So we can write two equations based on the number of leaves and flowers:

5x + 2y = 32 (equation 1)

y = 6 (equation 2)

We can substitute equation 2 into equation 1 to solve for x:

5x + 2(6) = 32

5x = 20

x = 4

So there are 4 plants with 5 leaves and (y=6) plants with 2 leaves and 1 flower. In total, there are 4+6 = 10 plants.