Use Tables of Equivalent Ratios Quick Check 4 of 54 of 5 Items 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 4; 8 4; 8 6; 16 6; 16 12; 16 12; 16 9; 12
The correct responses are:
For every 4 blue crayons in a box, there are 3 white ones. If there are 8 blue ones, we can find the number of white ones by setting up the ratio:
White/Blue = 3/4
Since there are 8 blue crayons, we can write the equation:
White/8 = 3/4
To solve for White, we can cross multiply:
4 * White = 8 * 3
4 * White = 24
White = 24/4 = 6
So, there are 6 white crayons if there are 8 blue ones.
Similarly, if there are 12 white crayons, we can set up the ratio:
White/Blue = 3/4
Since we want to find the number of blue crayons, we can write the equation:
12/Blue = 3/4
To solve for Blue, we can cross multiply:
4 * Blue = 12 * 3
4 * Blue = 36
Blue = 36/4 = 9
So, there are 9 blue crayons if there are 12 white ones.
To determine the number of white crayons if there are 8 blue ones, we can use the table of equivalent ratios. According to the table, for every 4 blue crayons, there are 3 white ones.
Since we have 8 blue crayons, we can set up a proportion:
4 blue crayons / 3 white crayons = 8 blue crayons / x white crayons
Cross multiplying, we get:
4x = 8 * 3
4x = 24
Dividing both sides by 4, we find:
x = 6
Therefore, there are 6 white crayons if there are 8 blue ones.
To determine the number of blue crayons if there are 12 white ones, we can use the same method. According to the table, for every 4 blue crayons, there are 3 white ones.
Setting up the proportion:
4 blue crayons / 3 white crayons = x blue crayons / 12 white crayons
Cross multiplying, we get:
4 * 12 = 3x
48 = 3x
Dividing both sides by 3, we find:
x = 16
Therefore, there are 16 blue crayons if there are 12 white ones.
To find the solution to these questions, we can use the table of equivalent ratios provided.
For the first question, "How many white crayons are there if there are 8 blue ones?", we need to find the ratio of white crayons to blue crayons. Looking at the table, we see that for every 4 blue crayons, there are 3 white ones. So, we can set up the ratio:
White to Blue = 3:4
To find the missing value, which is the number of white crayons, we can use cross-multiplication. Multiply 8 (the number of blue crayons) by the ratio of white to blue:
8 * (3/4) = 24/4 = 6
Therefore, there are 6 white crayons if there are 8 blue ones.
For the second question, "How many blue crayons are there if there are 12 white ones?", we set up the ratio:
White to Blue = 3:4
Again, using cross-multiplication, we can find the missing value, which is the number of blue crayons:
12 * (4/3) = 48/3 = 16
Therefore, there are 16 blue crayons if there are 12 white ones.
So, the correct responses are:
For the first question: 6; 16
For the second question: 6; 16