RATIOS AND RATES WORKSHEET

Problem 1 :

1360 grams of coffee cost $17.68. What is the unit price of the coffee per gram?

Problem 2 :

At a grocery store, 20 fl. oz. of brand A vitamin water is sold for $0.95. What is the unit price of the vitamin water per ounce, to the nearest cents?

Problem 3 :

Three angles of a triangle are in the ratio of 3 : 5 : 7. What is the measure of each angle?

Problem 4 :

The ratio of 7/4 to 5/2 is equal to the ratio 14 to what number?

Problem 5 :

If 2(x - y) = 3y, what is the ratio x/y?

Problem 6 :

The length and width of a rectangular garden are in the ratio 6 : 7. If the perimeter of the rectangle is 78 meters, what is the area of the garden in square meters?

Problem 7 :

If a car travels 218.5 miles on 9.5 gallons of gas, how many miles does the car travel on 15.5 gallons of gas? 

Problem 8 :

The density of aluminum is 2.7 grams per cm³. How many grams does 12 cm³ of aluminum weigh?

Problem 9 :

The ratio of Anne's height : Ben's height is 7 : 9. Anne's height is 1.4 m, find Ben's height.

Problem 10 :

There are some sweets in a bag. 18 of the sweets are toffees. 12 of the sweets are mints.

Write down the ratio of the number of toffees and mints

Give your answer in simplest form.

Problem 11 :

There are some oranges and apples in the box. The total number of oranges and apples is 54. The ratio of the number of oranges to the number of apples is 1 : 5. Work out the number of apples in the box.

Problem 12 :

The cost of 4 kg of broccoli is $5.52

The total cost of 3 kg of broccoli and 2.5 kg of carrots is $5.59. Workout 1 kg of carrots.

Answers

1. Answer :

$17.68/1360 grams  =  1768 cents/1360 grams

$17.68/1360 grams  =  1.3 cents/gram

The unit price of the coffee is 1.3 cents per gram.

2. Answer :

$0.95/20 fl. oz.  =  95 cents/20 fl. oz.

$0.95/20 fl. oz.  =  4.75 cents/fl. oz.

The unit price of the the vitamin water per ounce is about 5 cents. 

3. Answer :

From the ratio 3 : 5 : 7, the three angles are

2x, 7x, 11x 

In any triangle, sum of the angles is equal to 180°.

Then,

2x + 7x + 11x  =  180°

20x  =  180

Divide each side by 20.

x  =  9

Measure of each angle : 

First angle  =  2(9)  =  18°

Second angle  =  7(9)  =  63°

Third angle  =  11(9)  =  99°

4. Answer :

Let x be the required number. 

Then, 

7/4 : 5/2  =  14 : x

Write the above ratios as divisions. 

7/4 ÷ 5/2  =  14 ÷ x

(7/4) ⋅ (2/5)  =  14/x

7/10  =  14/x

7x  =  14 ⋅ 10

7x  =  140

Divide each side by 7.

x  =  20

So, the required number is 20.

5. Answer :

2(x - y)  =  3y

2x - 2y  =  3y

Add 2y to each side. 

2x  =  5y

Divide each side by 2y. 

2x/2y  =  5y/2y

x/y  =  5/2

6. Answer :

From the ratio 6 : 7, 

length  =  6x

width  =  7x

Given : Perimeter of the rectangle is 78 meters. 

2l + 2w  =  78

Substitute.

2(6x) + 2(7x)  =  78

12x + 14x  =  78

26x  =  78

Divide each side by 26.

x  =  3

Find the length and width : 

length  =  6(3)  =  18 meters

width  =  7(3)  =  21 meters

Area of the rectangle : 

=  l ⋅ w

Substitute. 

=  18 ⋅ 21

=  378

The area of the garden is 378 square meters.

7. Answer :

Distance covered on 9.5 gallons of gas  =  218.5 miles

Distance covered on 1 gallon of gas : 

=  218.5 / 9.5

=  23 miles

Distance covered on 15.5 gallons of gas : 

=  15.5 ⋅ 23

=  356.5 miles 

The car travels 356.5 miles on 15.5 gallons of gas. 

8. Answer :

Weight of 1 cm³ aluminum  =  2.7 grams

Weight of 12 cm³ aluminum : 

=  12 ⋅ 2.7 grams

=  32.4 grams

12cm³ of aluminum weighs 32.4 grams. 

9. Answer :

Anne's height : Ben's height = 7 : 9

Anne's height = 1.4 m

Ben's height = x

7 : 9 = 1.4 : x

7/9 = 1.4/x

x = 1.4(9/7)

x = 0.2(9)

x = 1.8 m

So, Ben's height is 1.8 m.

10. Answer :

Number of toffees = 18

Number of mints = 12

Ratio between number of toffees to number of mints

= 18 : 12

= 3 : 2

So, the required ratio is 3 : 2.

11. Answer :

The total number of oranges and apples = 54

Ratio between oranges to apples = 1 : 5

1x = number of oranges and 5x = number of apples

1x + 5x = 54

6x = 54

x = 54/6

x = 9

Number of oranges = 9

Number of apples = 5(9) ==> 45

The cost of 4 kg of broccoli = $5.52

Finding the cost of 1 kg of broccoli = 5.52/4

= $1.38

Cost of 3 kg of broccoli = 3(1.38)

= $4.14

Cost of 3 kg of broccoli + cost of 2.5 kg of carrots

= $5.59

4.14 +  cost of 2.5 kg of carrots = 5.59

cost of 2.5 kg of carrots = 5.59 - 4.14

= 1.45

Cost of 1 kg of carrot = 1.45/2.5

= $0.58

So, cost of 1 kg of carrot is $0.58.

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