Question

A box has 450 balls, each either white or black, there being as many metallic white balls as metallic black balls. If 40% of the white balls and 50% of the black balls are metallic, then the number of non-metallic balls in the box is

Answer 1

Let's denote the number of white balls as W and the number of black balls as B.
From the information given:
1. Metallic white balls = 0.40W
2. Metallic black balls = 0.50B

Given that the number of metallic white balls is equal to the number of metallic black balls, we have: 0.40W = 0.50B ... (i)
The total number of balls is W + B = 450 ... (ii)
From equation (i): $W = (\frac{5}{4})B$ ... (iii)

Substituting the value of W from equation (iii) into equation (ii):
$(\frac{5}{4})B + B = 450$

$\frac{(5B + 4B) }{ 4} = 450 9B = 1800$
B = 200

So, the number of black balls is 200 and the number of white balls is 450 - 200 = 250.

Using the percentage of metallic balls:
Number of metallic white balls = 0.40 x 250 = 100
Number of metallic black balls = 0.50 x 200 = 100

Now, non-metallic balls:
Non-metallic white balls = 250 - 100 = 150
Non-metallic black balls = 200 - 100 = 100

Total number of non-metallic balls = 150 + 100 = 250.
Thus, the box has 250 non-metallic balls.