Making a quantitative prediction :
We can use proportional reasoning to make quantitative predictions and compare options in real-world situations.
Example 1 :
An online poll for a movie site shows its polling results for a new movie. If a newspaper surveys 150 people leaving the movie, how many people can it predict will like the movie based on the online poll ? Is the movie site’s claim accurate if the newspaper has 104 people say they like the movie ?
Analyze Information :
The answer is a prediction for how many people out of 150 will like the movie based on the online poll. Also tell whether the 104 people that say they like the movie is enough to support the movie site’s claim.
List the important information :
• The online poll says 72% of movie goers like the new movie.
• A newspaper surveys 150 people.
Formulate a plan :
Use a proportion to calculate 72% of the 150 people surveyed.
72 out of 100 is how many out of 150 ?
Set up a proportion.
72/100 = x/150
Multiply both sides by 150
(72/100)(150) = (x/150)(150)
108 = x
The newspaper can predict that 108 out of 150 people will say they like the movie, based on the online poll.
Justify and Evaluate :
Since 108 is close to 104, the newspaper survey and the online poll show that about the same percent of people like the movie.
Example 2 :
On average, 24% of customers who buy shoes in a particular store buy two or more pairs. One weekend, 350 customers purchased shoes. How many can be predicted to buy two or more pairs ? If 107 customers buy more than two pairs, did more customers than normal buy two or more pairs ?
24 out of 100 is how many out of 350 ?
Set up a proportion.
24/100 = x/350
Multiply both sides by 350
(24/100)(350) = (x/350)(350)
84 = x
From the above calculation, it is clear that 84 out of 350 customers buy two or more pairs
Since 107 > 84, more customers than normal bought two or more pairs.
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