A grocer sells apples for $1.35 each, pears for $1.45 each, and oranges for $1.60 each. She also offers a discount of 70c for anyone who buys two pieces of fruit, and a discount of $1.60 for anyone who buys three pieces of fruit. One day she sells 50 pieces of each type of fruit, for a total of $202. How many customers did she have, assuming each customer bought 1,2 or 3 pieces of fruit?
Apple+Orange+Pineapple = $202
Under the primary principle of Diophantine, each fruit will fall under the peillian equations meaning the people had ((202/2*2^4)/128)+0.5
= 51
To solve this problem, let's consider the number of customers who bought 1, 2, or 3 pieces of fruit separately.
Let's start with the customers who bought 1 piece of fruit. Since the number of apples, pears, and oranges sold are the same, and the total number sold is 50 for each fruit type, we can deduce that 50/3 = 16.667 (approximately 16.67) customers bought 1 piece of fruit.
Next, let's consider the customers who bought 2 pieces of fruit. To maximize the number of customers who can take advantage of the discount, let's assume they bought two different types of fruit. The total discount for buying two pieces of fruit is 70 cents, so we can set up an equation:
2(1.35 + 1.45 + 1.6) - 0.70(x) = 202 - 50(1.35 + 1.45 + 1.6)
Simplifying the equation gives us:
2(4.40) - 0.70x = 202 - 200.5
8.80 - 0.70x = 1.5
-0.70x = 1.5 - 8.80
-0.70x = -7.3
x = -7.3 / -0.70
x ≈ 10.43
Approximately 10.43 customers bought 2 pieces of fruit. Since we can't have a fraction of a customer, let's round down to 10 customers.
Finally, let's consider the customers who bought 3 pieces of fruit. Again, to maximize the discount, let's assume they bought one of each fruit type. The total discount for buying three pieces of fruit is $1.60, so we can set up an equation:
3(1.35 + 1.45 + 1.6) - 1.60(x) = 202 - 50(1.35 + 1.45 + 1.6)
Simplifying the equation gives us:
3(4.40) - 1.60x = 202 - 200.5
13.20 - 1.60x = 1.5
-1.60x = 1.5 - 13.20
-1.60x = -11.70
x = -11.70 / -1.60
x ≈ 7.31
Approximately 7.31 customers bought 3 pieces of fruit. Since we can't have a fraction of a customer, let's round down to 7 customers.
Now let's add up the number of customers who bought 1, 2, or 3 pieces of fruit:
16.67 + 10 + 7 ≈ 33.67
Approximately 33.67 customers bought 1, 2, or 3 pieces of fruit. Since we can't have a fraction of a customer, let's round down to 33 customers.
Therefore, the grocer had approximately 33 customers who bought 1, 2, or 3 pieces of fruit in total.