Question

How many pieces 6 1/4 in. long can be cut from 35 metal rods each 40 in. long?

Answer 1

We want to cut pieces of length:

$l_P=6\frac{1}{4}in=(6+\frac{1}{4})in=(\frac{24}{4}+\frac{1}{4})in=\frac{25}{4}in=6.25in$

from 35 metal rods each 40in long, and we want to know how many we can cut.

In order to answer the question, we must compute the number of pieces that we can cut from each metal rod, and then multiply the result by the number of metal rods. Let's do that!

1) From each metal rod we can cut:

$\frac{l_R}{l_P}=\frac{40in}{6.25in}=6.4\rightarrow6\text{ pieces}$

2) We have 35 metal rods, so the total number of pieces of 6 1/4 in that we can cut is:

$35\cdot6=210$

Answer

We can cut 210 pieces from the 35 metal rods.

Remark: we see that by cutting the pieces we will have a waste of metal from each rod.