Question

Boden is making a prize wheel for the school fair. The diagram shows the ratio of winning spaces to non-winning spaces.

The table shows the numbers of winning and total spaces that could be on the wheel.
Based on the ratio, complete the missing values in the table.
Boden is making a prize wheel for the school fair. The diagram shows the ratio of winning spaces to non-winning spaces.
Winning spacesNon-winning spaces
A tape diagram with 2 tapes of unequal lengths. The first tape has 5 equal parts. A curved bracket above the first tape is labeled Winning spaces. The second tape has 6 equal parts of the same size as in the first tape. A curved bracket below the second tape is labeled Non-winning spaces.
The table shows the numbers of winning and total spaces that could be on the wheel.
Based on the ratio, complete the missing values in the table.
Winning spaces Total spaces
10 33

Answer 1

The student is dealing with ratio and proportion problem in order to complete the prize wheel table. By setting up proportions based on the provided ratio of winning to non-winning spaces, the missing total spaces corresponding to 10 and 33 winning spaces were found to be 22 and 73, respectively.

To solve this problem, we have to understand the relationship between the ratio of winning spaces to non-winning spaces and use it to complete the missing values in the table.

Given from the tape diagram:
- The ratio of winning spaces to non-winning spaces is 5:6.

This means that for every 5 winning spaces, there are 6 non-winning spaces on the wheel. Therefore, the total number of spaces for one set of this ratio is 5 (winning) + 6 (non-winning) = 11 total spaces.

Let's calculate the missing values in the table:

1. Calculate the number of total spaces when there are 10 winning spaces:
Since the ratio must be maintained, we can set up a proportion where 5 winning spaces correspond to 11 total spaces:

`(5 winning spaces )/(11 \\total \\spaces ) = (10 \\winning \\spaces)/(x total spaces)`

`(5)/(11) =(10)/(x)`
To solve for x, cross-multiply:
5 × x = 11 × 10
165 = 11y

`x = (110)/(5)`
x = 2

So, with 10 winning spaces, there are 22 total spaces on the prize wheel.

2. Calculate the number of winning spaces when there are a total of 33 spaces:
Again, using the same ratio, but this time we need to find out the number of winning spaces corresponding to a total of 33 spaces:

`(5 winning spaces )/(11 \\total \\spaces ) = (y \\winning \\spaces)/(33 total spaces)`

`(5)/(11) =(y)/(33)`
To solve for y, cross-multiply:
5 × 33 = 11 × y
165 = 11y

`y = (165)/(11)`
y = 15

So, when there are 33 total spaces, there are 15 winning spaces on the prize wheel.

Now we can complete the table with the missing values:

Winning spaces Total spaces
10 22
15 33