A trail mix recipe calls for 1 cup of nuts for every 2 cups of granola. If you want to make 12 cups of trail mix, how many cups of granola will you need? Use a tape diagram to help organize your thinking
It’s opening day at an amusement park. There are 132 people in line before it officially opens. If the ratio of adults to kids waiting to get in is 5:6 , how many kids are waiting in line? (1 point) Responses 60 kids 60 kids 12 kids 12 kids 72 kids 72 kids 66 kids
To find out how many kids are waiting in line, we need to split the total number of people waiting in line (132) according to the given ratio of adults to kids, which is 5:6.
Let's represent the number of adults as "A" and the number of kids as "K".
Based on the ratio, we can set up the equation: A : K = 5 : 6
To find the value of K, we need to determine the common multiple of 5 and 6. The smallest common multiple of 5 and 6 is 30.
So, if we multiply both sides of the equation by 6, we get:
6A : 6K = 5 : 6
Since the ratio is now equivalent to the total number of people waiting in line, we have:
6A + 6K = 132
We can simplify the equation to:
6(A + K) = 132
Dividing both sides of the equation by 6, we get:
A + K = 22
Now, we need to solve for K by isolating it on one side of the equation:
K = 22 - A
Since the number of kids (K) is what we want to find, we can substitute it with the value from the given ratio:
K = 22 - 5
K = 17
Therefore, there are 17 kids waiting in line.
To solve this problem, we can use a tape diagram to visually represent the ratio between nuts and granola in the trail mix recipe.
First, let's divide the total amount of trail mix we want to make (12 cups) into two equal parts: one part for nuts and one part for granola. We can use a tape diagram to represent this as shown:
Nuts Granola
_______ _______
Next, we know that the recipe calls for 1 cup of nuts for every 2 cups of granola. To represent this ratio, we can divide the nuts part of the diagram into pairs. Since each pair should have 1 cup of nuts and 2 cups of granola, we can add them to the diagram:
Nuts Granola
_______ _______
| | | | | |
| 1 | 1 | | | |
Now, we can see that for every 2 cups of granola, we need 1 cup of nuts. To find out how many cups of granola we need for 12 cups of trail mix, we can multiply the number of pairs of granola by 2:
Number of pairs of granola = Total cups of trail mix / Number of cups per pair
= 12 / 2
= 6
So, to make 12 cups of trail mix, we will need 6 pairs of granola. To find the total amount of granola needed, we multiply the number of pairs by the number of cups per pair:
Total cups of granola = Number of pairs * Number of cups per pair
= 6 * 2
= 12
Therefore, we will need 12 cups of granola to make 12 cups of trail mix.
What is the answers
To determine how many cups of granola will be needed, we need to understand the ratio given in the recipe, which is 1 cup of nuts for every 2 cups of granola.
Let's represent 1 cup of nuts as "N" and 2 cups of granola as "G".
To make 12 cups of trail mix, we need to find out how many "G" are needed.
We can set up a ratio equation:
N : G = 1 : 2
Since the recipe calls for 1 cup of nuts for every 2 cups of granola, we can multiply both sides of the equation by 6 (to make the ratio equivalent) since 6 * 2 = 12.
N * 6 : G * 6 = 1 * 6 : 2 * 6
6N : 6G = 6 : 12
Then we can simplify the equation to:
N : G = 1 : 2
So, to make 12 cups of trail mix, you will need 6 cups of granola.
Tape Diagram:
N : G
───┐ ┌───┐
1 ──┘ └───┘ 2
Each line on the tape diagram represents a cup. Since we want to make 12 cups, we can determine that we need 6 segments (or cups) of granola.
To determine the number of cups of granola needed to make 12 cups of trail mix, we can use a tape diagram to represent the ratio of nuts to granola in the recipe.
Let's start by representing 1 cup of nuts as one unit:
1 cup of nuts
According to the recipe, for every 2 cups of granola, we need 1 cup of nuts. Therefore, we can represent 2 cups of granola as two units:
1 cup of nuts
---------------
2 cups of granola
Now, since we want to make 12 cups of trail mix, we can multiply each side of the tape diagram by 6 to scale it up:
6 cups of nuts
----------------
12 cups of granola
Therefore, to make 12 cups of trail mix, we will need 12 cups of granola.