Final answer:
Mary must put back 5 oranges in order for the average price of the fruit she keeps to fall to 52 cents.
Step-by-step explanation:
To solve this, first we need to calculate the total cost of the 10 fruits: 10 fruits × 56 cents = 560 cents. We know that the price of an apple is 40 cents, and the price of an orange is 60 cents.
Let's assume Mary has 'x' oranges. Since she has a total of 10 fruits, this means she has (10 - x) apples. Now, let's calculate the total cost of the fruits based on the number of each fruit:
Total cost = (Number of apples × Price per apple) + (Number of oranges × Price per orange)
Total cost = ((10 - x) × 40) + (x × 60)
560 = 400 + 20x
Next, we solve for 'x' to find out how many oranges Mary originally had:
560 = 400 + 20x
160 = 20x
8 = x
Mary originally had 8 oranges and 2 apples.
Now, we want the new average price to be 52 cents, so the new total cost should be:
(10 - y) fruits × 52 cents = Total cost, where 'y' is the number of oranges Mary puts back.
Keeping in mind that she originally had 8 oranges, and we are looking for the number she puts back, we set up the following equation:
(10 - y) × 52 = 400 + 20 × (8 - y)
Solving for 'y' gives us:
520 - 52y = 400 + 160 - 20y
520 - 52y = 560 - 20y
160 - 32y = 0
5 = y
Mary must put back 5 oranges for the average price of the fruits she keeps to be 52 cents.
Complete question:
At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents?