Seventh Heaven Orchards decides to hold a special sale at the end of the season, hoping that people will come and buy the apples that have already fallen from the trees! They decide on an unusual system for pricing the apples. The bags they give out hold just seven apples each. The orchard then charges its customers five cents for every bag of seven apples, and 15 cents for every apple left over! According to this system, which costs the most: 10 apples, 30 apples, or 50 apples?
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To determine which option costs the most - 10 apples, 30 apples, or 50 apples - we need to calculate the cost of each quantity of apples using the given pricing system.
According to the pricing system, Seventh Heaven Orchards charges five cents for every bag of seven apples, plus 15 cents for every apple left over.
Let's calculate the cost for each option:
1. 10 Apples:
To calculate the cost for 10 apples, we need to divide it into bags of seven apples. We will have one bag that contains seven apples and three apples left over. Therefore, the cost for 10 apples would be equal to the price of one bag (5 cents) plus the price of three individual apples (3 * 15 cents).
Cost = 5 cents (1 bag) + 3 * 15 cents (3 apples)
Cost = 5 cents + 45 cents
Cost = 50 cents
2. 30 Apples:
Similarly, for 30 apples, we divide it into bags of seven apples. We will have four bags that contain twenty-eight apples and two apples left over. Therefore, the cost for 30 apples would be equal to the price of four bags (4 * 5 cents) plus the price of two individual apples (2 * 15 cents).
Cost = 4 * 5 cents (4 bags) + 2 * 15 cents (2 apples)
Cost = 20 cents + 30 cents
Cost = 50 cents
3. 50 Apples:
For 50 apples, we divide it into bags of seven apples. We will have seven bags that contain forty-nine apples and one apple left over. Therefore, the cost for 50 apples would be equal to the price of seven bags (7 * 5 cents) plus the price of one individual apple (1 * 15 cents).
Cost = 7 * 5 cents (7 bags) + 1 * 15 cents (1 apple)
Cost = 35 cents + 15 cents
Cost = 50 cents
Therefore, the cost is the same for all three options: 10 apples, 30 apples, and 50 apples. They all cost 50 cents.
Hint:
10 = 1*7 + 3
30 = 4*7 + 2
50 = 7*7 + 1