What is the ratio of solid chocolates to filled chocolates in a box where 2/3 of the nut-filled chocolates is 1/5 the total number of filled chocolates?
To find the ratio of solid chocolates to filled chocolates, we first need to determine the number of nut-filled chocolates. Let's denote the number of nut-filled chocolates as n.
According to the given information, 2/3 of the nut-filled chocolates is 1/5 of the total number of filled chocolates. Mathematically, this can be written as:
(2/3) * n = (1/5) * (n + n)
Simplifying this equation, we have:
2n/3 = 2n/5
To solve for n, we'll cross-multiply and solve for n:
5 * 2n = 3 * 2n
10n = 6n
Subtracting 6n from both sides, we have:
10n - 6n = 0
4n = 0
This equation tells us that n = 0. However, having zero nut-filled chocolates is not possible or meaningful, so there must be an error in the given information or equation.
Without a valid value for n, we cannot determine the ratio of solid chocolates to filled chocolates in the box.