Question

10 rubber stamps cost $10.30.
which equation would help determine the cost of 2 rubber stamps?
choose 1 answer:
a (\frac{2}{x} = \frac{$10.30}{10})
b (\frac{x}{2} = \frac{10}{$10.30})
c (\frac{2}{10} = \frac{$10.30}{x})
d (\frac{2}{$10.30} = \frac{x}{10})
e none of the above

Explanation:

Step1: Define variables

Let \( x \) be the cost of 2 rubber stamps. The cost per stamp should be the same, so we can set up a proportion. The number of stamps over the cost should be equal for both cases (10 stamps and 2 stamps).

Step2: Set up the proportion

For 10 stamps, the number of stamps is 10 and the cost is \(\$10.30\). For 2 stamps, the number of stamps is 2 and the cost is \( x \). So the proportion is \(\frac{2}{10}=\frac{x}{\$10.30}\)? Wait, no, let's check the options. Wait, option A: \(\frac{2}{x}=\frac{\$10.30}{10}\). Let's cross - multiply: \(2\times10 = x\times\$10.30\), so \(x=\frac{2\times10}{\$10.30}\), which is the cost of 2 stamps (since cost per stamp is \(\frac{\$10.30}{10}\), and for 2 stamps, \(x = 2\times\frac{\$10.30}{10}\), so rearranging \(\frac{2}{x}=\frac{\$10.30}{10}\) gives the correct proportion. Let's check other options:

• Option B: \(\frac{x}{2}=\frac{10}{\$10.30}\), cross - multiply: \(x\times\$10.30=2\times10\), \(x = \frac{20}{\$10.30}\), which is not the correct relation.
• Option C: \(\frac{2}{10}=\frac{\$10.30}{x}\), cross - multiply: \(2x = 10\times\$10.30\), \(x=\frac{10\times\$10.30}{2}\), which is the cost of 10 stamps times 5, not correct.
• Option D: \(\frac{2}{\$10.30}=\frac{x}{10}\), cross - multiply: \(2\times10=\$10.30\times x\), \(x = \frac{20}{\$10.30}\), incorrect.

So the correct proportion is in option A.

Answer:

A. \(\boldsymbol{\frac{2}{x}=\frac{\$10.30}{10}}\)