Final answer:
To make 28 pounds of clay into vases, we need to divide the total clay by the amount needed for each vase. The potter can make 18 vases with 28 pounds of clay.
Step-by-step explanation:
To find out how many vases can be made for 28 pounds of clay, we need to divide the total amount of clay by the amount needed for each vase. The amount needed for each vase is given as 3(9)/(20) pounds of clay. First, we need to convert this mixed number to an improper fraction. We can do this by multiplying the whole number (3) by the denominator (20) and adding the numerator (9). So, 3(9)/(20) is equal to 69/20 pounds of clay for each vase.
Now, we can divide the total amount of clay (28 pounds) by the amount needed for each vase (69/20 pounds). To divide by a fraction, we can multiply by the reciprocal. So, 28 pounds divided by 69/20 pounds is equal to 28 pounds multiplied by 20/69.
Using the multiplication rule, we can cancel out common factors between the numerator and denominator to simplify the calculations. In this case, both 28 and 20 are divisible by 4, and 69 is divisible by 3.
28 pounds multiplied by (20/69) is equal to (7 x 4) pounds multiplied by (5 x 4) / (3 x 23) pounds. Simplifying further, we get 7 x 5 / 23 pounds, which is approximately 1.52 pounds.
Therefore, based on these calculations, approximately 1.52 pounds of clay is needed for each vase. Since we have 28 pounds of clay, we can make 28 / 1.52 vases, which is approximately 18.42 vases. Since we cannot have a fraction of a vase, the potter can make 18 vases with 28 pounds of clay.