Given:
standards for direct materials in making a certain product are 20 pounds at $0.75 per pound. 56,000 units of product were made and the materials quantity variance was $30,000
30,000 / 0.75 per pounds = 40,000 pounds
The materials quantity variance of $30,000 infers that 40,000 pounds were used inefficiently.
56,000 units x 20 pounds = 1,120,000 pounds used
total pounds used: 1,120,000 + 40,000 = 1,160,000 pounds
The number of pounds of direct materials used during the period is 1,160,000 pounds.