The price of 10 pounds of apples is d dollars. If the apples weigh an average of 1 pound for every 6 apples, which of the following is the average price, in cents, of a dozen such apples? The answer should be one of the following but I don't know how to set the problem up to solve it.
20d
50d over 3
5d
5d over 3
d over 20
10 lbs of apples = 10 x 6 = 60 apples
so the average price per apple is
d/60 dollars = 100 x d /60 cents
so a dozen apples would be
12 x 100 x d / 60 cents
To solve this problem, we need to figure out the price of one apple and then calculate the average price of a dozen apples.
Given that the price of 10 pounds of apples is d dollars, we can determine the price of one pound of apples by dividing the total price by the total weight. Since there are 10 pounds of apples, the price per pound is d/10 dollars.
Now, we need to find the price of one apple. We know that there are 6 apples for every pound, so the price of one apple is (d/10)/6 dollars.
To calculate the average price of a dozen apples, we multiply the price of one apple by 12 (since a dozen is equal to 12). Therefore, the average price of a dozen apples is 12 * [(d/10)/6] dollars.
To simplify this expression, we can divide the numerator and denominator inside the parentheses by 2:
Average price of a dozen apples = 12 * [(d/10)/6] dollars
= 12 * (d/60) dollars
= d/5 dollars.
To convert the average price to cents, we multiply by 100 (since there are 100 cents in a dollar):
Average price of a dozen apples = (d/5) * 100 cents
= 20d cents.
Therefore, the average price of a dozen such apples is 20d cents.
To solve the problem and find the average price of a dozen apples, we need to set up an equation using the given information.
We are told that the price of 10 pounds of apples is d dollars. So, the price per pound of apples is d/10 dollars.
We are also told that the average weight of 1 pound of apples is equivalent to 6 apples. Therefore, the average weight of each apple is 1/6 pounds.
Now, we can find the price of one apple by dividing the price per pound by the weight of one apple. Thus, the price of one apple is (d/10)/(1/6) which simplifies to (6d)/(10), or (3d)/(5) dollars.
To find the average price of a dozen apples, we need to multiply the price of one apple by 12 (since there are 12 apples in a dozen). Therefore, the average price of a dozen apples is (3d/5) * 12.
Simplifying this expression, we have:
(3d/5) * 12 = 36d/5
Now, we need to convert this fraction to cents since the answer options are given in cents. To convert from dollars to cents, we multiply by 100. So, we have:
(36d/5) * 100 = (3600d)/5
Simplifying further, we get:
(3600d)/5 = 720d
Therefore, the average price of a dozen apples in cents is 720d.
Therefore, none of the given answer options match the correct answer.