Sure, let's solve this problem step-by-step.
To determine the total number of steel rods purchased by the machine shop, we need to sum the quantities of rods for each diameter.
1. Number of rods of [tex]\( \frac{7}{8} \)[/tex]-in. diameter:
There are 14 rods of [tex]\( \frac{7}{8} \)[/tex]-in.-diameter.
2. Number of rods of [tex]\( \frac{1}{2} \)[/tex]-in. diameter:
There are 23 rods of [tex]\( \frac{1}{2} \)[/tex]-in.-diameter.
3. Number of rods of [tex]\( \frac{1}{4} \)[/tex]-in. diameter:
There are 8 rods of [tex]\( \frac{1}{4} \)[/tex]-in.-diameter.
4. Number of rods of 1-in. diameter:
There are 19 rods of 1-in.-diameter.
Now, to find the total number of rods, we will add these quantities together:
[tex]\[
14 + 23 + 8 + 19
\][/tex]
Let's perform the addition step-by-step:
[tex]\[
14 + 23 = 37
\][/tex]
[tex]\[
37 + 8 = 45
\][/tex]
[tex]\[
45 + 19 = 64
\][/tex]
Therefore, the total number of rods purchased by the machine shop is 64.
