Tape Diagrams Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
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Question
A new superhero movie has its first showing and there are 155 people in line to see it. If the ratio of kids to adults waiting to see this movie is 3:2 , how many adults are in line? Use a tape diagram to help organize your thinking.(1 point)
adults
To solve this problem using a tape diagram, we will represent the number of kids and adults as two separate bars, with the ratio of 3:2.
First, we divide 155 into 5 equal parts (since the ratio is 3:2):
155 ÷ 5 = 31
Then, we multiply this value by 2 to find the number of adults:
31 x 2 = 62
Therefore, there are 62 adults in line.
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I apologize, I made a mistake in my previous response. Let me correct it.
To solve this problem using a tape diagram, we will represent the number of kids and adults as two separate bars, with the ratio of 3:2.
First, we divide the total number of people in line, 155, into 5 equal parts (since the ratio is 3:2):
155 ÷ 5 = 31
Next, we multiply this value by 2 to find the number of adults:
31 x 2 = 62
Therefore, there are 62 adults in line.
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.(1 point)
cups
To solve this problem using a tape diagram, we will represent the amount of nuts and granola as two separate bars, with the ratio of 1:2.
Since the ratio is in terms of cups, we can assume the unit of measurement is already the same for both nuts and granola.
We know that for every 1 cup of nuts, we need 2 cups of granola. Therefore, the ratio can be represented as:
1 cup of nuts : 2 cups of granola
To find out how many cups of granola are needed to make 12 cups of trail mix, we divide 12 by the sum of the parts in the ratio (1 + 2 = 3):
12 ÷ 3 = 4
This means that for every 1 part in the ratio, we need 4 cups of trail mix. Since the ratio states that we need 2 parts of granola, we multiply 4 by 2:
4 x 2 = 8
Therefore, you will need 8 cups of granola to make 12 cups of trail mix.
An animal shelter has cats and dogs available for adoption in a ratio of 3:5 . If there are 25 dogs available for adoption, how many cats are available? Use a tape diagram to help organize your thinking.(1 point)
cats
To solve this problem using a tape diagram, we will represent the number of cats and dogs as two separate bars, with the ratio of 3:5.
The ratio states that for every 3 cats, there are 5 dogs. So, if we know there are 25 dogs available for adoption, we can use that information to find out how many cats are available.
First, we divide the number of dogs by the part of the ratio that represents the dogs:
25 ÷ 5 = 5
This means that each part of the ratio represents 5 dogs.
Next, we multiply the number we found in the previous step by the part of the ratio that represents the cats:
5 x 3 = 15
Therefore, there are 15 cats available for adoption.
Nate is helping to redesign his basement. He is in charge of choosing and buying the paint. He wants a specific shade of green, so he is going to combine blue and yellow paint in the ratio of 1:3 . If he needs 8 gallons of paint, how much yellow paint does he need to buy?
(1 point)
Responses
4 gallons
4 gallons
6 gallons
6 gallons
24 gallons
24 gallons
2 gallons
To solve this problem, we will set up a proportion using the ratio of blue to yellow paint.
The ratio of blue to yellow paint is 1:3, which means for every 1 unit of blue paint, there are 3 units of yellow paint. We also know that Nate needs a total of 8 gallons of paint.
Let's set up the proportion:
1/3 = x/8
To solve for x (the amount of yellow paint), we cross-multiply:
3 * x = 1 * 8
3x = 8
Next, we isolate x by dividing both sides of the equation by 3:
x = 8/3
So, Nate needs to buy 8/3 gallons of yellow paint, which is approximately 2.67 gallons.
Therefore, the correct answer is 2 gallons.
Ruthie plays on a travel soccer league. For every 7 shots she takes on goal, she scores twice. If she scores 8 times, how many shots on goal did she take?
(1 point)
Responses
56 shots
56 shots
8 shots
8 shots
36 shots
36 shots
28 shots
28 shots
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To solve this problem, we can set up a proportion using the ratio of shots on goal to goals scored.
The ratio of shots on goal to goals scored is 7:2, which means for every 7 shots on goal, Ruthie scores 2 goals. We also know that she scored 8 times.
Let's set up the proportion:
7/2 = x/8
To solve for x (the number of shots on goal), we cross-multiply:
2 * x = 7 * 8
2x = 56
Next, we isolate x by dividing both sides of the equation by 2:
x = 56/2
So, Ruthie took 28 shots on goal.
Therefore, the correct answer is 28 shots.
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
12 kids
12 kids
66 kids
66 kids
72 kids
72 kids
60 kids
To solve this problem using a ratio, we can set up a proportion using the ratio of adults to kids waiting in line.
The ratio of adults to kids is 5:6, which means for every 5 adults, there are 6 kids. We also know that there are 132 people in line.
Let x represent the number of kids in line.
The proportion can be set up as:
5/6 = x/132
To solve for x (the number of kids), we cross-multiply:
6 * x = 5 * 132
6x = 660
Next, we isolate x by dividing both sides of the equation by 6:
x = 660/6
x = 110
So, there are 110 kids waiting in line.
Therefore, the correct answer is 110 kids.
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
12 kids
12 kids
66 kids
66 kids
72 kids
72 kids
60 kids
To solve this problem, we can set up a proportion using the given ratio of adults to kids waiting in line.
The ratio of adults to kids is 5:6, which means for every 5 adults, there are 6 kids. We also know that there are 132 people in line.
Let x represent the number of kids in line.
The proportion can be set up as:
5/6 = x/132
To solve for x, we cross-multiply:
6x = 5 * 132
6x = 660
Now, divide both sides of the equation by 6:
x = 660/6
x = 110
Therefore, there are 110 kids waiting in line.
The correct answer is 110 kids.
Ladamier's eyes widened with surprise as he processed his father's words.
Ladamier's eyes widened with surprise, and he took a moment to process his father's words.
Edgar is making an egg casserole for brunch. He needs eggs and sausages in the ratio of 3:2 . If he is going to use 12 eggs, how many sausages does he need?
(1 point)
Responses
20 sausages
20 sausages
5 sausages
5 sausages
8 sausages
8 sausages
12 sausage
To solve this problem using a ratio, we can set up a proportion using the given ratio of eggs to sausages.
The ratio of eggs to sausages is 3:2, which means for every 3 eggs, there are 2 sausages. We also know that Edgar is going to use 12 eggs.
Let x represent the number of sausages needed.
The proportion can be set up as:
3/2 = 12/x
To solve for x (the number of sausages), we cross-multiply:
2 * 12 = 3 * x
24 = 3x
Next, we isolate x by dividing both sides of the equation by 3:
x = 24/3
x = 8
Therefore, Edgar needs 8 sausages for the casserole.
The correct answer is 8 sausages.
A clothing store has pants and shorts for sale in a ratio of 4:3 . If there are a total of 70 pants and shorts available for sale, how many of those are shorts?
(1 point)
Responses
21 shorts
21 shorts
30 shorts
30 shorts
10 shorts
10 shorts
40 shorts
40 shorts
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To solve this problem using a ratio, we can set up a proportion using the given ratio of pants to shorts.
The ratio of pants to shorts is 4:3, which means for every 4 pants, there are 3 shorts. We also know that there are a total of 70 pants and shorts available for sale.
Let x represent the number of shorts.
The proportion can be set up as:
4/3 = (70 - x)/x
To solve for x (the number of shorts), we cross-multiply:
3 * (70 - x) = 4 * x
210 - 3x = 4x
Now, add 3x to both sides of the equation:
210 = 7x
Next, divide both sides of the equation by 7:
x = 210/7
x = 30
Therefore, there are 30 shorts available for sale.
The correct answer is 30 shorts.