Question

The fruit seller is packing oranges into some bags. If he packs 5 oranges into each bag, he has 14 oranges leftover. If he packs 7 oranges into each bag, he will need another 2 bags. How many oranges does the fruit seller have​

Answer 1

Penjelasan dengan langkah-langkah:

Let's start by using algebra to solve the problem.

Let n be the total number of oranges the fruit seller has.

If he packs 5 oranges into each bag, then the number of bags he can fill completely is n/5, and he will have n%5 (n modulo 5) oranges leftover.

According to the problem, he has 14 oranges leftover when packing 5 oranges per bag, so we can write:

n%5 = 14

If he packs 7 oranges into each bag, then the number of bags he can fill completely is n/7, and he will need n/7 + 2 bags to pack all the oranges.

According to the problem, he needs another 2 bags when packing 7 oranges per bag, so we can write:

n/7 + 2 = n/5 - 1

Now we can use these two equations to solve for n:

n%5 = 14 -> n = 5k + 14 (for some integer k)

n/7 + 2 = n/5 - 1 -> 5n + 70 = 7n - 35 -> n = 52

Therefore, the fruit seller has 52 oranges.