Question

Lily's colored-pencil box has 2 shades of red pencils and 5 shades of blue pencils. Joseph's box has 1 shade of red

pencils and 4 shades of blue pencils. Lily thinks that the ratio of red pencils to blue pencils is the same for both
boxes, because they each have 3 more shades of blue pencils than shades of red pencils. Is the same ratio of
shades of red pencils to shades of blue pencils maintained? Justify your response.
Select Choice Lily's ratio is Select Choice Select Choice and Joseph's is Select Choice Select Choice

Answer 1

Let’s assume that the number of red pencils in Lily’s box is r and the number of blue pencils is b. Similarly, let’s assume that the number of red pencils in Joseph’s box is r’ and the number of blue pencils is b’.

According to the problem statement, we have:

r = 2

b = 5

r’ = 1

b’ = 4

b - r = b’ - r’

b - r = 3

We can use the above information to form two equations:

r/b = r’/b’

b - r = 3

Solving these equations, we get:

r’/b’ = 2/5

r/b = 2/5

r’ = 2

b’ = 5

Therefore, the ratio of shades of red pencils to shades of blue pencils is maintained in both boxes.

Hope this helped :)