Question

In Kelly's pencil pouch, she has 7 mechanical pencils and 4 regular pencils. Makenna has 6 mechanical pencils

and 2 regular pencils. Kelly thinks that the ratio of mechanical to regular pencils in both pencil pouches is the
same because they each have four more mechanical than regular pencils. Is the ratio of mechanical to regular
pencils the same? Justify your reasoning.
; Kelly's ratio is
to
5
2
to 3
To be an equivalent ratio
Makenna's ratio is

Answer 1

Kelly's ratio of mechanical to regular pencils is 7:4, while Makenna's is 6:2, which simplifies to 3:1. These two ratios are not equivalent, since 7:4 is not the same as 3:1, demonstrating that the proportion of pencils differs between the two pouches.

Step-by-step explanation:

The student asked whether the ratio of mechanical to regular pencils is the same in Kelly's and Makenna's pencil pouches. To answer this, we must compare the ratios. For Kelly, the ratio of mechanical to regular pencils is 7 to 4, or 7/4 when simplified. For Makenna, the ratio of mechanical to regular pencils is 6 to 2, which simplifies to 3 to 1 or 3/1. To compare ratios and determine if they are equivalent, we can set up a proportion.

Since the question includes irrelevant information regarding measurement and the metric system, we will ignore that and focus on the ratios presented. Setting the two ratios equal to each other like 7/4 = 3/1 will show that they are not equivalent. Kelly's thinking is incorrect because even though they each have four more mechanical than regular pencils, the proportions of mechanical to regular pencils are different. Kelly's ratio is 7:4, whereas Makenna's ratio is 6:2, which simplifies to 3:1, showing a different relationship between the number of mechanical to regular pencils.