Question

Boden is making a prize wheel for the school fair. The ratio of winning spaces to losing spaces is shown in the diagram. The table shows the number of winning and losing spaces that could be on the wheel. Based on the ratio, complete the missing values in the table.

Answer 1

The correct answers are Losing 12; Winning 15

Explanation:

The ratio of winning to losing is 5: 6 or 5/6. This means for every 5 winning spaces in the wheel there are 6 losing spaces. This ration should be used to complete the values of the table.

1. The first row shows there are 10 winning and you need to calculate the number of losing spaces. The process is shown below.

$\frac{5}{6} = \frac{10}{x}$ - Express the ratios using fractions; use x to show the missing value

$5x = 60$ - Cross multiply to find the value of x

$x = 60 / 5$ - Solve the equation to find x

$x = 12$ - The number of losing is 12 if there are 10 winning spaces

2. The second row shows there are 18 losing spaces, and you need to calculate the number of winning spaces. Repeat the process.

$\frac{5}{6} = \frac{x}{18}$

$6x = 90$

$x = 90 / 6$

$x =15$ - The number of winning spaces is 15 if there are 18 losing spaces

Answer 2

Answer:

Step-by-step explanation:

There will be 5 winning spaces for every losing spaces on the wheel. The values in the table represent ratios that are equivalent to this rate. If there are 222 times as many winning spaces, there will also be 222 times as many losing spaces. If there are 333 times as many losing spaces, there will also be 333 times as many winning spaces.