Solve Mixture Problems with Ratios Quick Check
2 of 52 of 5 Items
Question
Use the table to answer the question.
Apples 5 40 50
Bananas 6 12 60
The table shows the number of apples to bananas in a mixture. What are the missing values?
(1 point)
Responses
15 apples and 40 bananas
15 apples and 40 bananas
10 apples and 48 bananas
10 apples and 48 bananas
48 apples and 10 bananas
48 apples and 10 bananas
40 apples and 15 bananas
The missing values are 15 apples and 40 bananas.
To find the missing values in the table, we can determine the missing numbers by assessing the ratios between apples and bananas.
Looking at the table, the ratio between the first set of numbers (5 apples and 6 bananas) is 5/6.
So, applying the same ratio, we can calculate the missing values using the given numbers in the table.
For the first missing value, which is the number of apples corresponding to 12 bananas, we can set up a proportion as follows:
5 apples / 6 bananas = x apples / 12 bananas
Cross-multiplying, we get:
6x = 5 * 12
Simplifying, we have:
6x = 60
Dividing both sides by 6, we find:
x = 10
Therefore, the missing value is 10 apples and 12 bananas.
Similarly, for the second missing value, which is the number of bananas corresponding to 40 apples, we set up another proportion:
5 apples / 6 bananas = 40 apples / x bananas
Cross-multiplying, we get:
5x = 6 * 40
Simplifying, we have:
5x = 240
Dividing both sides by 5, we find:
x = 48
Therefore, the missing value is 40 apples and 48 bananas.
So, the correct answer is:
10 apples and 12 bananas, and
40 apples and 48 bananas.
Therefore, the correct response is:
10 apples and 48 bananas.
To solve this problem, we need to determine the missing values in the table.
First, let's look at the ratios given in the table. The ratio of apples to bananas is 5:6, and the ratio of bananas to apples is 12:40.
To find the number of missing apples, we can set up the following proportion:
5/6 = x/12
Where x represents the number of missing apples.
To solve for x, we can cross-multiply:
6x = 5 * 12
6x = 60
Dividing both sides of the equation by 6 gives us:
x = 10
So the missing value for apples is 10.
To find the number of missing bananas, we can use a similar approach. We set up the following proportion:
12/40 = y/5
Where y represents the number of missing bananas.
Cross-multiplying:
40y = 12 * 5
40y = 60
Dividing both sides by 40:
y = 1.5
However, since the table represents whole numbers of apples and bananas, we can round 1.5 to the nearest whole number, which is 2.
Therefore, the missing values are 10 apples and 2 bananas.
Looking at the given options, the correct answer is:
10 apples and 48 bananas.