Question
Use the image to answer the question.
An illustration shows two number lines with eight ticks marked on them at equal distances. The first number line, labeled vinegar, has the first two ticks on the left marked as 0 and 3, respectively. The second number line, labeled baking soda, has the first, second, and seventh ticks marked as 0, 1, and 6, respectively.
The ratio of parts of vinegar to baking soda for a cleaning mixture is 3 to 1. How many parts of vinegar are needed if there are 6 parts of baking soda?
(1 point)
Responses
8
8
19
19
18
18
3
The correct response is 18.
To determine how many parts of vinegar are needed if there are 6 parts of baking soda, we need to use the ratio of 3 to 1.
First, we observe that on the vinegar number line, there are 8 ticks, with the second tick marked as 3.
On the baking soda number line, there are also 8 ticks, with the seventh tick marked as 6.
Since the ratio of vinegar to baking soda is 3 to 1, we can see that the tick on the vinegar number line that corresponds to 6 parts of baking soda would be 2, as 6 divided by 3 equals 2.
Thus, if there are 6 parts of baking soda, we would need 2 parts of vinegar.
To answer the question, we need to determine the number of parts of vinegar needed when there are 6 parts of baking soda, based on the given ratio of 3 to 1.
First, let's look at the number line for baking soda. We see that the tick marks labeled 0 and 6 represent the two ends, with other tick marks in between. This means that the total length of the number line represents the 6 parts of baking soda.
Next, let's look at the number line for vinegar. We see that the tick marks labeled 0 and 3 represent the two ends, with other tick marks in between. This means that the total length of the number line represents the 3 parts of vinegar.
Since the ratio of vinegar to baking soda is 3 to 1, we can determine the number of parts of vinegar needed when there are 6 parts of baking soda by setting up a proportion.
The proportion is: (parts of vinegar) / (parts of baking soda) = (length of vinegar number line) / (length of baking soda number line)
Substituting the values we have:
(parts of vinegar) / 6 = 3 / 1
Cross-multiplying:
1 * (parts of vinegar) = 3 * 6
(parts of vinegar) = 18
Therefore, 18 parts of vinegar are needed when there are 6 parts of baking soda.