Math 8 Challenge : Proportion Word Problems



Ratio Word Problems

1) Express each of the following ratios as simply as possible in the form a : b.

a) 10 : 6 b) 24 : 8 c) 3.5 : 2.1 d)

2) Find the ratio of each of the following.

a) 20 cm to 1 m b) 1 kg to 70 g c) 80 m to 1 km d) 2 h to 45 min

3) Find the missing term.

a) 5 : 9 = 1 : x b) 6 : 8 = 21 : x c) 6 : 16 : 8 = x : y : 2

4) There are 5 boys to every 6 girls in a class of 44 pupils. Find the number of boys in the class.

5) If the ratio of the sides of 2 squares is 2 : 3, find the ratio of their areas.

6) Four people chipped in to buy a lottery ticket in the ratio 4 : 2 : 3 : 6. The ticket won $84 000. Calculate the first person’s share of the winnings.

7) A sum of $24 000 is to be divided into three shares in the ratio of 3 : 5 : 7.

Find the largest share.

8) The lengths of the sides of a triangle are in the ratio of 4 : 5 : 6. If the perimeter is 45 cm, find the sides.

9) A tree of height 45 m casts a shadow of 30 m. Then the height, in metres, of a tree casting a 28 m shadow is...?

10) A scale of a map reads 1 : 250 000. Find the distance, in km, between two towns which are

3.5 cm apart on the map.

11) The sides of a right angled triangle are 5 cm, 12 cm, and 13 cm. A rectangle has sides 6 cm

and 10 cm. Find the ratio of the area of the triangle to the area of the rectangle.

Rate word problems

1. Complete the following.

a) If a car travels 100 km in 4 hours, the rate of travel is ___ km/h

b) If one dozen eggs is sold for $2.40, the rate is ___ cents per egg.

c) If a tap fills a 450 litre tank with water in 1 hour, the water flows at the

rate of ___ litres per minute.

d) If $24.00 is charged for 120 kWh of electricity consumed, the rate is ___ cents/kWh.

2. If an airplane travels at a speed for 450 km/h, how many metres does it travel in 10 s?

3. Complete the following.

a) 30 km/h = ____ cm/sec

b) $100 per km = ____ cents per m

c) $2.50 per litre = ____ cents per ml

4. If one American dollar is worth 0.862 Canadian, then how much is one Canadian dollar worth in American?

5. If John Daly can drive the golf ball 329 yards, which is equivalent to 301 meters, then how

many yards would Mrs. Pugsley’s 280 m drive be?

6. I can go 15 m in 6 seconds. What is the average speed in km/h?

Answers.

Ratios

1) a) 5 : 3

b) 3 : 1

c) 5 : 3

d) 8 : 3

2) a) 1 : 5

b) 100 : 7

c) 2 : 25

d) 8: 3

3) a) 1.8

b) 28

c) x=1.5 y=4

4) 20

5) 4 : 9

6) $22 400

7) $11 200

8) 12cm, 15cm, 18cm

9) 42 m

10) 8.75 km

11) 1 : 2

Rates

1. a) 25 km/h

b) 20 cents

c) 7.5 l/min

d) 20 cents

2. 1250 m

3. a) 833⅓ cm/sec

b) 10 cents/min

c)¼ cents/ml

4. $1.16

5. 306 yards

6. 9 km/h

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Math 8

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