Use Tables of Equivalent Ratios Quick Check
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Question
Use the table to answer the question.
White Blue
3 4
x 8
9 12
12 y
For every 4 blue crayons in a box, there are 3 white ones. How many white crayons are there if there are 8 blue ones? How many blue crayons are there if there are 12 white ones?
(1 point)
Responses
9; 12
9; 12
4; 8
4; 8
6; 16
6; 16
12; 16
12; 16
The correct answer is 6; 16. For every 4 blue crayons, there are 3 white ones. Therefore, if there are 8 blue crayons, there would be 6 white crayons (8 divided by 4 equals 2, and 2 multiplied by 3 equals 6). If there are 12 white crayons, there would be 16 blue crayons (12 divided by 3 equals 4, and 4 multiplied by 4 equals 16).
To answer the question, we need to find the equivalent ratios between white and blue crayons and use them to determine the number of white crayons when there are 8 blue ones, and the number of blue crayons when there are 12 white ones.
Looking at the table, we can see that the ratio of white to blue crayons is constant throughout:
White : Blue
3 : 4
x : 8
9 : 12
12 : y
To find the missing values, we can set up proportions using the given ratios and cross-multiply.
1) To find the number of white crayons when there are 8 blue ones:
3/4 = x/8
To solve for x, we cross-multiply:
4 * x = 3 * 8
4x = 24
x = 24/4
x = 6
Therefore, there are 6 white crayons if there are 8 blue ones.
2) To find the number of blue crayons when there are 12 white ones:
3/4 = 12/y
To solve for y, we cross-multiply:
3 * y = 4 * 12
3y = 48
y = 48/3
y = 16
Therefore, there are 16 blue crayons if there are 12 white ones.
So the correct answers are:
How many white crayons are there if there are 8 blue ones? -> 6
How many blue crayons are there if there are 12 white ones? -> 16
To answer the first question, "How many white crayons are there if there are 8 blue ones?", you need to find a ratio in the table where the blue crayon count is 8.
Looking at the table, you can see that for every 4 blue crayons, there are 3 white ones. Since 8 is double of 4, you can also double the corresponding white crayon count.
So, if there are 8 blue crayons, there would be 2 sets of 4 blue crayons. And if each set has 3 white crayons, then the total number of white crayons would be 2 times 3, which equals 6.
Therefore, the answer is 6.
To answer the second question, "How many blue crayons are there if there are 12 white ones?", you need to find a ratio in the table where the white crayon count is 12.
Looking at the table, you can see that for every 3 white crayons, there are 4 blue ones. Since 12 is a multiple of 3, you can also multiply the corresponding blue crayon count.
So, if there are 12 white crayons, there would be 4 sets of 3 white crayons. And if each set has 4 blue crayons, then the total number of blue crayons would be 4 times 4, which equals 16.
Therefore, the answer is 16.
Hence, the correct answer is: 6; 16