Question

iara makes salad dressing by mixing 8 spoonfuls of oil and some vinegar. the tape diagram shows the ratio of oil to vinegar. oil vinegar complete the table. original ratio amount (spoonfuls) oil 8 vinegar 1 total dressing 3

Explanation:

Step1: Analyze the tape diagram

The tape diagram for oil has 2 equal parts, and vinegar has 1 part. So the ratio of oil to vinegar is \( 2:1 \), and total ratio parts are \( 2 + 1=3 \), which matches the total ratio given (3).

Step2: Find the ratio for oil

From the tape diagram, oil has 2 parts, vinegar 1 part, total 3 parts. So oil's original ratio is 2.

Step3: Find vinegar amount

The ratio of oil to vinegar is \( 2:1 \). Let vinegar amount be \( x \). We know oil is 8, so \( \frac{8}{x}=\frac{2}{1} \). Cross - multiply: \( 2x = 8\times1\), so \( x=\frac{8}{2}=4 \).

Step4: Find total dressing amount

Total ratio parts are 3. The ratio of oil to total is \( 2:3 \). Let total be \( y \). \( \frac{8}{y}=\frac{2}{3} \). Cross - multiply: \( 2y = 8\times3\), so \( y=\frac{24}{2}=12 \). Or we can add oil and vinegar amounts: \( 8 + 4=12 \).

Answer:

For the table:

• Oil's original ratio: \( 2 \)
• Vinegar's amount: \( 4 \)
• Total dressing's amount: \( 12 \)