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 cm3How many grams does 12 cm3 of aluminum weigh?

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 cmaluminum  =  2.7 grams

Weight of 12 cmaluminum : 

=  12 ⋅ 2.7 grams

=  32.4 grams

12cm3 of aluminum weighs 32.4 grams. 

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