Crystal mixed orange juice, fruit punch concentrate, and ginger ale in the ratio of 2:2:4 to make a special drink. To make 4 liters, how much of each ingredient should she use?

1L orange, 1L punch, 2L ginger ale

2L orange, 2L punch, 4L ginger ale

8L orange, 8L punch, 16L ginger ale

2L orange, 1L punch, 1L ginger ale

One out of three students in the school owns a cat. Of these students one out of two owns a fish. What fraction of the students owns both a cat and a fish?

1/6 of all students own both a cat and a fish.

1/2 of all students own both a cat and a fish.

5/6 of all students own both a cat and a fish.

3/4 of all students own both a cat and a fish.

1/4 of all students own both a cat and a fish.

Chapter 4: Ratio, Rate And Proportion

1.

1. Johnny has a bag full of marbles that he keeps in his desk. He has 35 red marbles and 25 green marbles. Find the ratio of red marbles to green marbles, and put it in its simplest form.
- A.
  
  35:25
- B.
  
  7:5
- C.
  
  25:35
- D.
  
  5:7
- E.
  
  6:5
Correct Answer
B. 7:5

Explanation
The ratio of red marbles to green marbles is found by dividing the number of red marbles by the number of green marbles. In this case, there are 35 red marbles and 25 green marbles. Dividing both numbers by 5 gives us a ratio of 7:5, which is the simplest form of the ratio.

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2
1
2.

If it costs $90 to feed a family of 3 for one week, how much will it cost to feed a family of 5 for one week?
- A.
  
  $180.00
- B.
  
  $30.00
- C.
  
  $120.00
- D.
  
  $150.00
Correct Answer
D. $150.00

Explanation
To find the cost of feeding a family of 5 for one week, we can use the concept of proportion. If it costs $90 to feed a family of 3 for one week, we can set up the proportion: 3/90 = 5/x, where x is the cost of feeding a family of 5 for one week. By cross-multiplying, we get 3x = 450, and dividing both sides by 3, we find that x = $150.00. Therefore, it will cost $150.00 to feed a family of 5 for one week.

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3.

In a school there are four boy scouts to every three girl scouts. If there are forty-two girl scouts, how many boy scouts are there?
- A.
  
  56 boy scouts
- B.
  
  56 girl scouts
- C.
  
  31.5 girl scouts
- D.
  
  31.5 boy scouts
- E.
  
  48 boy scouts
Correct Answer
A. 56 boy scouts

Explanation
Since there are four boy scouts for every three girl scouts, the ratio of boy scouts to girl scouts is 4:3. If there are 42 girl scouts, we can set up a proportion to find the number of boy scouts. Let x be the number of boy scouts. Then, we can write the proportion as 4/3 = x/42. Cross-multiplying, we get 4 * 42 = 3 * x, which simplifies to 168 = 3x. Dividing both sides by 3, we find that x = 56. Therefore, there are 56 boy scouts.

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4
1
4.

To make green paint, Jack mixes yellow paint and blue paint in the ratio of three to two. If he used twelve gallons of yellow paint, how much blue paint did he use?
- A.
  
  4
- B.
  
  6
- C.
  
  7
- D.
  
  8
- E.
  
  12
Correct Answer
D. 8

Explanation
Jack mixes yellow paint and blue paint in the ratio of three to two. This means that for every three gallons of yellow paint, he uses two gallons of blue paint. If he used twelve gallons of yellow paint, he would need to use eight gallons of blue paint (12 divided by 3 multiplied by 2) to maintain the ratio. Therefore, the correct answer is 8.

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5.

On a triangle, each side measures 5 cm, 10 cm, and 30 cm, respectively. In lowest terms, find the ratios of the lengths of the sides.
- A.
  
  1:2:6
- B.
  
  5:10:30
- C.
  
  .5:1:3
- D.
  
  5/10/30
Correct Answer
A. 1:2:6

Explanation
The ratios of the lengths of the sides of the triangle are 1:2:6. This means that the length of the first side is one unit, the length of the second side is two units, and the length of the third side is six units.

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6.

Crystal mixed orange juice, fruit punch concentrate, and ginger ale in the ratio of 2:2:4 to make a special drink. To make 4 liters, how much of each ingredient should she use?
- A.
  
  2L orange, 2L punch, 4L ginger ale
- B.
  
  8L orange, 8L punch, 16L ginger ale
- C.
  
  2L orange, 1L punch, 1L ginger ale
- D.
  
  1L orange, 1L punch, 2L ginger ale
Correct Answer
D. 1L orange, 1L punch, 2L ginger ale

Explanation
Crystal mixed orange juice, fruit punch concentrate, and ginger ale in the ratio of 2:2:4. This means that for every 2 parts of orange juice, she used 2 parts of fruit punch concentrate and 4 parts of ginger ale. To make 4 liters of the special drink, she would need to use 1 liter of orange juice, 1 liter of fruit punch concentrate, and 2 liters of ginger ale.

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1
2
7.

Brandon received $50 dollars for his paper route. He spent $20 dollars at the movies, and $10 dollars buying comic books then after buying $5 worth of popcorn, he saved the rest. What is the ratio of the amount of money spent buying comic books and popcorn, to the amount that saved?
- A.
  
  10:5:15
- B.
  
  15:15
- C.
  
  1:1
- D.
  
  2:1:3
- E.
  
  1:2:3
Correct Answer
C. 1:1

Explanation
The ratio of the amount of money spent buying comic books and popcorn to the amount saved is 1:1. This means that for every dollar spent on comic books and popcorn, Brandon saved an equal amount. In this case, he spent a total of $10 on comic books and popcorn, and he saved the rest, which is $40. Therefore, the ratio is 10:40, which simplifies to 1:4. However, since the answer choices only provide ratios with three terms, the ratio is simplified further to 1:1.

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3
3
8.

In Canada there is one car for every 1.9 people. How many car tires per person are there?
- A.
  
  40/19:1
- B.
  
  2:1
- C.
  
  4:1
- D.
  
  40:19
Correct Answer
A. 40/19:1

Explanation
The answer 40/19:1 suggests that for every 40 car tires, there are 19 people. This can be interpreted as there being approximately 2.11 car tires per person in Canada.

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1
0
9.

One out of three students in the school owns a cat. Of these students one out of two owns a fish. What fraction of the students owns both a cat and a fish?
- A.
  
  1/6 of all students own both a cat and a fish.
- B.
  
  1/2 of all students own both a cat and a fish.
- C.
  
  5/6 of all students own both a cat and a fish.
- D.
  
  3/4 of all students own both a cat and a fish.
- E.
  
  1/4 of all students own both a cat and a fish.
Correct Answer
A. 1/6 of all students own both a cat and a fish.

Explanation
The fraction of students who own both a cat and a fish can be calculated by multiplying the fractions of students who own a cat and who own a fish. Since one out of three students owns a cat and one out of two students owns a fish, the fraction of students who own both can be calculated as (1/3) * (1/2) = 1/6. Therefore, 1/6 of all students own both a cat and a fish.

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10.

A rectangle measures 20cm at its width and 5 cm at its length. Find the ratio of the length to the width to the perimeter of the rectangle in lowest form.
- A.
  
  1:4: 2.5
- B.
  
  4:1:10
- C.
  
  5:20:50
- D.
  
  20:5:50
- E.
  
  None of the above
Correct Answer
A. 1:4: 2.5

Explanation
Perimeter Calculation: We first calculate the perimeter of the rectangle using the formula: perimeter equals twice the sum of the length and width. In this case, the width of the rectangle is 20 cm, and the length is 5 cm. So, the perimeter is found by doubling the sum of these values, resulting in a perimeter of 50 cm.
Ratio Formation: The ratio we're asked to find involves three parts: the length, the width, and the perimeter of the rectangle. To express this ratio, we compare the length to the width and to the perimeter.
Expression in Lowest Terms: We express the ratio in its simplest form. For the length to width part, it's 1 to 4 because the length is one-fourth the size of the width. The width to itself is 1 since it's the same value. And for the perimeter to the width, it's 5 halves or 2.5 because the perimeter is 2.5 times the width.

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0
0

Chapter 4: Ratio, Rate And Proportion

1. Johnny has a bag full of marbles that he keeps in his desk. He has 35 red marbles and 25 green marbles. Find the ratio of red marbles to green marbles, and put it in its simplest form.

If it costs $90 to feed a family of 3 for one week, how much will it cost to feed a family of 5 for one week?

In a school there are four boy scouts to every three girl scouts. If there are forty-two girl scouts, how many boy scouts are there?

To make green paint, Jack mixes yellow paint and blue paint in the ratio of three to two. If he used twelve gallons of yellow paint, how much blue paint did he use?

On a triangle, each side measures 5 cm, 10 cm, and 30 cm, respectively. In lowest terms, find the ratios of the lengths of the sides.

Crystal mixed orange juice, fruit punch concentrate, and ginger ale in the ratio of 2:2:4 to make a special drink. To make 4 liters, how much of each ingredient should she use?

Brandon received $50 dollars for his paper route. He spent $20 dollars at the movies, and $10 dollars buying comic books then after buying $5 worth of popcorn, he saved the rest. What is the ratio of the amount of money spent buying comic books and popcorn, to the amount that saved?

In Canada there is one car for every 1.9 people. How many car tires per person are there?

One out of three students in the school owns a cat. Of these students one out of two owns a fish. What fraction of the students owns both a cat and a fish?

A rectangle measures 20cm at its width and 5 cm at its length. Find the ratio of the length to the width to the perimeter of the rectangle in lowest form.