Math  /  Numbers & Operations

Question6. In a flower garden, 40%40 \% of the plants are rosebushes. The garden has 60 rosebushes. How many plants are in the flower garden?

Studdy Solution

STEP 1

What is this asking? If we know 40% of the garden is 60 rose bushes, how many plants are there in total? Watch out! Don't mix up the part (rose bushes) with the whole (all plants).

STEP 2

1. Set up the percentage equation
2. Solve for the total number of plants

STEP 3

Let xx be the **total number of plants** in the garden.
This is what we're trying to find!

STEP 4

We're given that 40% of the plants are rose bushes.
To work with percentages in equations, we convert them to decimals.
So, 40% becomes 40100=0.40\frac{40}{100} = 0.40.
Remember, we're dividing by one hundred!

STEP 5

We know that 40% *of* the total number of plants (xx) *is* equal to the number of rose bushes (60). "Of" means multiply, and "is" means equals.
So, our equation is 0.40x=600.40 \cdot x = 60.

STEP 6

To get xx by itself, we need to divide *both* sides of the equation by 0.400.40.
Remember, we want to divide to one, so we can have 1x1 \cdot x, which is just xx.
So, we have 0.40x0.40=600.40\frac{0.40 \cdot x}{0.40} = \frac{60}{0.40}.

STEP 7

Now, we just need to do the division: 600.40=6040100=6010040=600040=150\frac{60}{0.40} = \frac{60}{\frac{40}{100}} = \frac{60 \cdot 100}{40} = \frac{6000}{40} = 150.
So, x=150x = 150!

STEP 8

There are a total of **150 plants** in the flower garden.

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