William and Daphne, both have crackers for a snack. The ratio of Williams crackers to Daphne‘s is 3 : 5 if there are 48 crackers total how many crackers does Daphne have you use a tape diagram to help organize your thinking
To represent the given ratio using a tape diagram, we can draw three sections for William's crackers and five sections for Daphne's crackers. Each section will represent an equal amount of crackers.
Let's say each section represents x crackers.
Since the total number of crackers is given as 48, the equation becomes:
3x + 5x = 48
Combining like terms:
8x = 48
Dividing both sides of the equation by 8:
x = 6
Therefore, each section represents 6 crackers.
To find out how many crackers Daphne has, we need to multiply the number of sections representing Daphne's crackers (5 sections) by the number of crackers represented by each section (6 crackers).
Daphne has 5 sections * 6 crackers = 30 crackers.
Thus, Daphne has 30 crackers.
To use a tape diagram to solve this problem, we can visually represent the ratio of William's crackers to Daphne's crackers. Each unit in the tape diagram can represent a certain number of crackers.
Step 1: Determine the ratio
The ratio of William's crackers to Daphne's crackers is given as 3:5.
Step 2: Divide the tape diagram
We can divide the tape diagram into 8 equal parts (3 + 5) to represent the total number of parts in the ratio.
Step 3: Assign values
Since the total number of crackers is given as 48, we can assign a value of 48 to the 8 equal parts in the tape diagram. Each part represents 48/8 = 6 crackers.
Step 4: Fill in the tape diagram
Using the assigned values, we can fill in the tape diagram as follows:
- Three parts (representing William's crackers) = 3 x 6 = 18 crackers
- Five parts (representing Daphne's crackers) = 5 x 6 = 30 crackers
So, Daphne has 30 crackers.
To solve this problem using a tape diagram, we can draw two rectangles representing William's and Daphne's crackers, respectively.
Let's start by representing the ratio of William's crackers to Daphne's, which is 3 : 5. We can break the rectangles into equal parts according to this ratio.
First, let's label the rectangles:
- Rectangle 1 represents William's crackers.
- Rectangle 2 represents Daphne's crackers.
Since we know that the total number of crackers is 48, we represent this with a line across both rectangles, dividing them into equal parts.
Now, divide Rectangle 1 into three equal parts by drawing two vertical lines inside the rectangle. These three parts represent the 3 parts in the ratio 3 : 5.
Similarly, divide Rectangle 2 into five equal parts by drawing four vertical lines inside the rectangle.
Counting the number of parts in Rectangle 2, we can see that Daphne has 5 parts out of 8 (3 + 5 = 8).
To find out how many crackers Daphne has, we divide the total number of crackers by the number of parts and multiply it by Daphne's share (5/8).
So, Daphne has (5/8) * 48 crackers.
Now we can calculate it:
Daphne has (5/8) * 48 = 30 crackers.
Therefore, Daphne has 30 crackers.