I planted red flowers in 0.6 of her
garden. I also planted yellow flowers in 0.4
of my garden. In 0.5 of the part with red
flowers she also planted white flowers. What
part of my garden has both red and
white flowers? How should I solve this in pictures
To solve this problem using pictures, we can represent the gardens as a rectangle divided into equal parts. Let's assume the rectangle represents the entire garden and each part of the rectangle represents an equal area.
First, let's divide the garden into 10 equal parts:
```
__ __ __ __ __ __ __ __ __ __
| | | | | | | | | | |
|__|__|__|__|__|__|__|__|__|__|
```
Next, we planted red flowers in 0.6 of her garden. So shade in 6 out of 10 parts to represent the red flowers:
```
__ __ __ __ __ __ __ __ __ __
|__|__|__|__|__|__| | | | |
|__|__|__|__|__|__|__|__|__|__|
```
Then, we planted yellow flowers in 0.4 of my garden. Shade in 4 out of 10 parts to represent the yellow flowers:
```
__ __ __ __ __ __ __ __ __ __
|__|__|__|__|__|__|__|__|__|__|
|__|__|__|__|__|__|__|__|__| |
```
Now, we know that in the part with red flowers, she also planted white flowers in 0.5 of that area. Divide the shaded part representing red flowers into 2 equal parts and shade 1 part to represent white flowers:
```
__ __ __ __ __ __ __ __ __ __
|__|__|__|__|__|__|__| | | |
|__|__|__|__|__|__|__|__|__| |
```
The shaded area where red and white flowers overlap represents the part of your garden that has both red and white flowers. In this case, it is 1 out of 10 parts:
```
__ __ __ __ __ __ __ __ __ __
|__|__|__|__|__|__|__|__|__|__|
|__|__|__|__|__|__|__|__|__|X |
```
Therefore, 0.1 or 1/10 of your garden has both red and white flowers.
To solve this visually, you can represent the garden as a rectangle or a square. Divide the garden into parts based on the proportions mentioned in the problem.
Step 1: Draw a rectangle or square to represent the garden.
Step 2: Divide the garden into two parts, according to the proportions mentioned. Since you planted red flowers in 0.6 of her garden and yellow flowers in 0.4 of your garden, you can divide the garden into two parts in this ratio. You can draw a horizontal line to separate the two parts, with the top part representing her garden and the bottom part representing your garden.
Step 3: In the part representing her garden, divide it again based on the 0.5 proportion mentioned. Draw a vertical line in the top part (her garden) to create two equal parts. The left part will represent the part with red flowers, and the right part will represent the part with red and white flowers.
Step 4: Now, to determine the part of your garden that has both red and white flowers, you need to look at the corresponding part in your garden that mirrors the part with red and white flowers in her garden. This will be the bottom right part of the garden, as it mirrors the top right part of her garden.
Step 5: Shade or color the bottom right part of your garden to represent the part that has both red and white flowers.
This visual representation will help you understand which part of your garden has both red and white flowers.
To solve this problem and understand it visually, you can use a rectangular grid or diagram to represent the gardens.
1. Start by drawing a rectangle to represent the total area of your garden. Label it as "My Garden."
2. Divide the rectangle horizontally into two parts, one representing the portion of your garden where you planted red flowers and the other part where you planted yellow flowers. Label the red flower section accordingly.
3. Within the red flower section, divide it vertically into two parts. One part will represent the area where white flowers were planted, and the other part where only red flowers were planted.
4. Label the section with white flowers accordingly.
Now let's find the part of your garden that has both red and white flowers.
In your garden, you planted red flowers in 0.6 of its total area. So shade in 60% of the red flower section you drew initially.
Next, you know that in 0.5 of the part with red flowers, she also planted white flowers. Since the proportion is given based on the red flower section, shade in half of the white flower section you drew within the red flower part.
Count the shaded area where both red and white flowers are present in your garden. This shaded area represents the portion of your garden that has both red and white flowers.
To determine the exact proportion, divide the count of the shaded area by the total area of your garden.
By visually representing the problem in a rectangular grid, you can easily determine the part of your garden that has both red and white flowers and also understand the proportion using the shaded areas.