John, Lucy and Emma share 60 pencils in a ratio of 4:5:6. How many pencils does Lucy receive?

60 pencils are distributed to John, Lucy and Emma in the proportion of 4:5:6.
First, add the numbers given in the proportion to get a denominator to use, in this case: 4 + 5 + 6 = 15.
Then, use 15 as the denominator to express each part in a fraction:
John gets \(\frac{\mathrm{4} }{\mathrm{15}}\) of the 60 pencils.
Lucy gets \(\frac{\mathrm{5} }{\mathrm{15}}\) of the 60 pencils.
Emma gets \(\frac{\mathrm{6} }{\mathrm{15}}\) of the 60 pencils.
Multiply Lucy’s fraction by the total number of pencils (60) to get the number of Lucy’s pencils:
\(\frac{\mathrm{5}}{\mathrm{15}} \times 60 = 20 pencils\)