In a wallet containing gold, silver and bronze tokens, the ratio of gold to silver tokens was 5:17 while the ratio of bronze to gold tokens was 18:19. What was the ratio of bronze to silver tokens?

The correct option is 90:323.

Step-by-Step Explanation:

Step 1: Understand the given ratios

We are given the following ratios of tokens in the wallet:

Ratio of Gold (G) to Silver (S) tokens:

$\frac{\text{G}}{\text{S}}=\frac{5}{17}$

Ratio of Bronze (B) to Gold (G) tokens:

$\frac{\text{B}}{\text{G}}=\frac{18}{19}$

Step 2: Find the ratio of Bronze to Silver tokens

To find the ratio of Bronze to Silver tokens (B:S), we can multiply the ratio of Bronze to Gold by the ratio of Gold to Silver:

$\frac{\text{B}}{\text{S}}=\frac{\text{B}}{\text{G}}\times \frac{\text{G}}{\text{S}}$

Step 3: Substitute the given values into the equation

$\frac{\text{B}}{\text{S}}=\frac{18}{19}\times \frac{5}{17}$

Step 4: Perform the multiplication

Multiply the numerators and the denominators:

Numerator = 18 × 5 = 90

Denominator = 19 × 17 = 323

Thus, the ratio is:

$\frac{\text{B}}{\text{S}}=\frac{90}{323}$

Therefore, the ratio of bronze to silver tokens is 90:323.