To find the rate at which the machine makes nails in pounds per hour, we need to divide the amount of nails by the time taken to make them.
The machine makes 2 1/4 pounds of nails in 1 1/2 hours.
To convert 2 1/4 to an improper fraction, we multiply the whole number (2) by the denominator (4) and add the numerator (1), then write the result over the denominator:
2 1/4 = (2 x 4 + 1)/4 = 9/4
To convert 1 1/2 to an improper fraction, we multiply the whole number (1) by the denominator (2) and add the numerator (1), then write the result over the denominator:
1 1/2 = (1 x 2 + 1)/2 = 3/2
Now we can divide the amount of nails by the time:
(9/4) ÷ (3/2) = (9/4) x (2/3) = 18/12 = 3/2
Therefore, the machine makes nails at a rate of 3/2 pounds per hour. The correct answer is C.