Question

4 markers cost $7.04.
which equation would help determine the cost of 7 markers?
choose 1 answer:
a $\frac{4}{7} = \frac{$7.04}{x}$
b $\frac{x}{7} = \frac{4}{$7.04}$
c $\frac{7}{x} = \frac{$7.04}{4}$
d $\frac{4}{7} = \frac{x}{$7.04}$
e none of the above

Explanation:

Step1: Define the relationship

Let \( x \) be the cost of 7 markers. The cost per marker should be constant. So, the ratio of the number of markers to the cost should be equal. For 4 markers, the ratio is \( \frac{4}{\$7.04} \), and for 7 markers, the ratio is \( \frac{7}{x} \). Wait, no, actually, the ratio of number of markers to cost for 4 markers is \( \frac{4}{\$7.04} \), and for 7 markers, it's \( \frac{7}{x} \). But let's check the options. Option A: \( \frac{4}{7}=\frac{\$7.04}{x} \). Let's see, cross - multiply: \( 4x = 7\times\$7.04 \), which means \( x=\frac{7\times\$7.04}{4} \), which is the correct way to find the cost of 7 markers (since cost per marker is \( \frac{\$7.04}{4} \), then cost of 7 markers is \( 7\times\frac{\$7.04}{4} \), and the proportion \( \frac{4}{7}=\frac{\$7.04}{x} \) is equivalent to that).

Let's analyze each option:

• Option A: \( \frac{4}{7}=\frac{\$7.04}{x} \). Cross - multiplying gives \( 4x = 7\times7.04 \), which is a valid proportion because the ratio of the number of markers (4 to 7) should be equal to the ratio of their costs (\( \$7.04 \) to \( x \)) since the cost per marker is constant.
• Option B: \( \frac{x}{7}=\frac{4}{\$7.04} \). Cross - multiplying gives \( x\times\$7.04=4\times7 \), which would give \( x = \frac{28}{\$7.04} \), which is incorrect.
• Option C: \( \frac{7}{x}=\frac{\$7.04}{4} \). Cross - multiplying gives \( 7\times4=x\times\$7.04 \), or \( x=\frac{28}{\$7.04} \), which is incorrect.
• Option D: \( \frac{4}{7}=\frac{x}{\$7.04} \). Cross - multiplying gives \( 4\times\$7.04 = 7x \), or \( x=\frac{4\times\$7.04}{7} \), which is incorrect.

Answer:

A. \( \frac{4}{7}=\frac{\$7.04}{x} \)