Ratio/Rate

Question

Suppose 40 out 90 people are bowlers annd 3 out of 16 of the bowlers have their own bowling ball. At the same rate in a group of 192 people, predict how many you would expect to have a bowling ball.

Answer 1

Hi John,

 

Let's begin by finding the number of bowlers expected out of 192 people by solving this proportion:

    bowlers : people = bowlers : people

    40 : 90 = x : 192

    (40)(192) = (90)(x)

    90x = (40)(192)

    9x = (4)(192)

    9x = 768

    x = 768/9

    x = 85 and 1/3 (round down to nearest whole #)

    x = 85 bowlers 

 

Now let's find out how many of these bowlers we can expect to have a bowling ball by solving this proportion:

    bowling balls : bowlers = bowling balls : bowlers

    3 : 16 = x : 85

    (3)(85) = (16)(x)

    16x = (3)(85)

    16x = 255

    x = 255/16

    x = 15 and 15/16 (round up to nearest whole #)

    x = 16 bowlers with a bowling ball

 

The key here was using our answer found from one proportion as the input to another proportion to get our answer.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.

Answer 2

Here's what we know:

192 * 40/90 * 3/16

There are 192 people, of them there 40/90 of the populace as bowlers, and of that, 3/16 are ball owners.

Let's start simplifying:

40 and 90 share a 10:

192 * 4/9 * 3/16

 

4 and 16 share a 4:

192 * 1/9 * 3/4

 

9 and 3 share a 3:

192 * 1/3 * 1/4

 

192 and 3 share a 3:

64 * 1/1 * 1/4

64/4

16

 

So there will be about 16 people who own a bowling ball of their own.