The table below shows the number of pencils and pens three friends have in their backpacks. Who has a greater ratio of pencils to pens?
A. Lydia
B . Angel
C . Elizabeth

Angel has a greater ratio of pencils to pens.

i.e. Angle's pencils to pens = 3 / 2 or 63/42

Thus, option (B) is true.

Step-by-step explanation:

Considering the table

Lydia's Number of Pencils = 10

Lydia's Number of Pens = 7

Lydia's Pencils to Pens ratio = 10/7

Angel's Number of Pencils = 9

Angel's Number of Pens = 6

Angels's Pencils to Pens ratio = 9/6 = 3 / 2

Elizabeth's Number of Pencils = 12

Elizabeth's Number of Pens = 9

Elizabeth's Pencils to Pens ratio = 12/9 = 4 / 3

So, We get the inputs ratios such as:

Lydia's ratio:  Angels's ratio: Elizabeth's ratio

      10/7      :         3 / 2         :        4 / 3

As the least common denominator (LCD) is: 42

Rewriting as equivalent fractions with the LCD:

10/7            :         3 / 2         :        4 / 3

60 / 42       :        63/42       :       56/42

Sorting from least to greatest:

Sorting this table by the numerators of the equivalent fractions in order from least to greatest:

Elizabeth's ratio       :         Lydia's ratio       :    Angels's ratio:  

4/3                             :         10 /7                  :        3 / 2

56/42                        :          60 / 42             :         63/42

Therefore, Angel has a greater ratio of pencils to pens.

i.e. Angle's pencils to pens = 3 / 2 or 63/42

Thus, option (B) is true.