Question

In word problems that have a multiplicative comparison problem structure, two different sets are compared, and one of the sets consists of multiple copies of the other set.

Which of the following best illustrates a word problem that has a multiplicative comparison problem structure?
a) Marcus drives 3 times as many miles to get to work as Hannah does. Hannah drives 16 miles to get to work. How many miles does Marcus drive to get to work?

b) The length of a rectangular garden is 4 times the width. If the width of the garden is 5 meters, what is the length of the garden?

c) Sarah has 5 times as many books as Mark. If Mark has 8 books, how many books does Sarah have?

d) A car travels at a speed that is 6 times faster than a bicycle. If the bicycle is moving at a speed of 10 kilometers per hour, what is the speed of the car?

Answer 1

Option (a) is a multiplicative comparison word problem where Marcus drives 3 times as many miles as Hannah does, and if Hannah drives 16 miles, Marcus drives 48 miles to work.

Step-by-step explanation:

The word problem that best illustrates a multiplicative comparison problem structure is (a) Marcus drives 3 times as many miles to get to work as Hannah does. Hannah drives 16 miles to get to work. How many miles does Marcus drive to get to work? In this problem, two different sets are compared: the distance Hannah drives and the distance Marcus drives. The distance Marcus drives is described as multiple copies (3 times) of the distance Hannah drives.

To solve this, you multiply the distance Hannah drives by the factor that Marcus's distance is greater (3 times Hannah's distance). So, Marcus drives 3 × 16 miles, which equals 48 miles to work.