8rachel decided to have bouncy balls as a party favor. she determines that her ratio of bouncy balls to guests is 9: 3. explain how to find the number of balls needed for 30 guests.

The second value of the ratio is guests, which is currently 3. To make this 30, you would multiply it by 10, and do the same to the first value, representing bouncy balls, to get the number of balls necessary for 30 people to maintain the same ratio. 9 * 10 = 90, so 90 balls would be required if the same ratio is to be kept.

Identify the variables as number of guests, x, to the number of bouncy balls, y. The ratio, 9:3, can be simplified to 3:1 resulting in the constant of variation of 3. The equation y = 3x is used to substitute the 30 guests in for x, y = 3(30), y= 90, so she needs 90 bouncy balls for 30 guests.