Solve the Problem by Writing an Equation

177: Solve the problem by writing an equation.

Winnie bought 2 packets of biscuits. She also bought some candies with 12 dollars. She spent 60 dollars altogether. How much does each packet of biscuits cost?

Let x dollars be the cost of each packet of biscuits.

Checking: Each packet of biscuits costs dollars.

2 packets cost dollars. The candies cost dollars.

Thus, Winnie spent dollars altogether.

There were 4 rolls of cloth of the same length in a factory. Workers used 68 metres from one of the rolls to make jackets. The total length of cloth left is 280 metres. How long was each roll of cloth originally?

Let x metres be the original length of each roll of cloth.

Checking: Each roll of cloth was metres long originally.

There were metres in 4 rolls. metres of cloth were used.

metres of cloth are left.

A train travelled 208 km in 4 hours. What was the average speed of the train?

Let x km/h be the average speed of the train.

Checking: The average speed of the train was km/h.

It travelled km in 4 hours.

Ms Lee bought 2 roses and 1 tulip. She paid 42 dollars altogether. If the cost of a tulip is 10 dollars, how much does a rose cost?

Let n dollars be the cost of each rose.

Checking: Each rose costs dollars. A tulip costs dollars.

The total cost of 2 roses and 1 tulip is dollars.

A watermelon weighs 3.6 kg. It is 0.2 kg lighter than a honeydew melon. How many kilograms does the honeydew melon weigh?

Let w kg be the weight of the honeydew melon.

Checking: The watermelon weighs kg. It is kg lighter than the honeydew melon.

The honeydew melon weighs kg.

182: Solve the problem by writing an equation. Mandy is 1.52 m tall. She is 0.03 m taller than Felix. How tall is Felix?

Let h m be the height of Felix.

Checking: Felix is m tall. Mandy is m tall.

Mandy is m taller than Felix.

Workers have repaired 85.2 m of a road. 18.7 m of the road is not repaired yet. How long is the road?

Let l metres be the length of the road.

Checking: The road is m long. Workers have repaired m of the road.

m of the road is not repaired yet.

Mary bought some preserved beef and pork with 12.5 dollars. The preserved pork costs 7.8 dollars. How much does the preserved beef cost?

Let x dollars be the cost of preserved beef.

Checking: The preserved pork costs dollars. The preserved beef costs dollars.

They cost dollars altogether.

There is a roll of ribbon. After cutting 0.8 m, there is 1.5 m left. How long was the original ribbon?

Let x metres be the original length of the ribbon.

Checking: The original ribbon was m long. m of the ribbon is cut.

m of the ribbon are left.

186: Solve the problem by writing an equation. There are different kinds of books in a book shop. Of which 800 copies are textbooks. If the number of supplementary exercise books is doubled, there are 28 copies more than textbooks. How many supplementary exercise books are there?

Let y copies be the number of supplementary exercise books.

Checking: There are copies of textbooks and copies of supplementary exercise books.

Doubling the number of story books is copies more than the number of textbooks.

The perimeter of a piece of rectangular paper is 80 cm. Its width is 16 cm. What is its length?

Let y cm be the length of the piece of paper.

Checking: The length and width of the rectangle are cm and cm respectively.

The perimeter of the rectangle is cm.

The area of a piece of grassland in the shape of a parallelogram is 72 m2. The length of its base is 12 m. What is its height?

Let x metres be its height.

Checking: The length and height of the grassland are m and m respectively.

The area of the grassland is m2.

3 There is a bundle of flowers. of them are roses and the rest are lilies. If 4 there are 8 lilies, how many flowers are there in the bundle?

Let p be the number of flowers in the bundle.

1 There is a box of juicy candies. of them are orange flavour, 3 of them 5 10 are strawberry flavour. There are 60 candies of orange flavour and

Let x be the number of candies in the box.

There is a big sale in a supermarket. There is a 10% discount for all washing powder. Mother bought a box of washing powder and she paid 3.8 dollars less. What is the original cost of the box of washing powder?

Let P dollars be the original cost of this box of washing powder.

Ming has 15 marbles. He bought another 2 bags of marbles. Then he has 127 marbles altogether. How many marbles are there in each bag?

Let y be the number of marbles in each bag.

The savings of Lily are 3 dollars less than 4 times that of Mary. Lily has 105 dollars. How much does Mary have?

Let x dollars be the savings of Mary.

A teacher shared a bag of biscuits equally among Susan, Mary and Peter. After Peter has eaten 8 pieces, he still has 13 pieces left. How many pieces of biscuits were there in the bag?

Let x be the number of biscuits in the bag.

6 Mother has a bag of salt. She gave of it to Mrs. Fong. After using 200 11 grams, Mrs. Fong still has 340 grams left. How many grams of salt were there in the bag at first?

Let y grams be the weight of salt in the bag at first.

Three people shared the costs of buying a detective story at 98 dollars and a set of fairy tales. Each has to pay 69 dollars. How much is the set of fairy tales?

Let M dollars be the cost of the set of fairy tales.

There is a big sale in a supermarket. For each pack of sausages bought, 2 sausages will be given free. Cindy bought 4 packs of sausages and she got a total of 36 sausages. How many sausages are there in each pack originally?

Let x be the number of sausages in each pack.

There is a sale in a department store. Ms Lee bought a handbag with 50 dollars reduction. She has another 15% discount because she has a VIP card. Finally, Ms Lee paid 561 dollars for this handbag. What is the original price of this handbag?

Let c dollars be the original price of the handbag.

2 Timmy has some marbles. Susan has 26 marbles, which is of Timmy’s 7 marbles after he bought 30 more marbles. How many marbles did Timmy have at first?

Let N be the number of marbles Timmy had.

There is a rectangle of 3 cm wide and its perimeter is 18 cm. Find its length.

Let x cm be the length of the rectangle.

Gigi and Mimi each has a square handkerchief. The length of each side of Gigi’s handkerchief is 2 cm shorter than that of Mimi’s. The perimeter of Gigi’s handkerchief is 60 cm. What is the length of each side of Mimi’s handkerchief?

Let y cm be the length of each side of Mimi’s handkerchief.

There is a trapezium. Its lower base is 14 cm and its height is 8 cm. Its area is 152 cm2. How long is its upper base? Let x cm be the length of the upper base of the trapezium.

There is a sticker in the shape of a trapezium. The upper base and the lower base are 7 cm and 10 cm long respectively. If its height is increased by 2 cm, its area becomes 68 cm2. Find the height of the sticker.

Let y cm be the height of the sticker.

There was a bag of rice. After eating 3.3 kg of rice, 1.7 kg of rice were left. How many kilograms of rice were there originally?

Let R kg be the original weight of the bag of rice. R – 3.3 = 1.7 R – 3.3 + = 1.7 +

∴ There were kg of rice originally.

Checking: There were kg of rice originally. 3.3 kg of rice were eaten.

kg of rice were left.

269: Solve the problem by writing an equation. 2 tin of tea weighs 520 grams. Find the weight of the whole tin of tea. 3

Let T grams be the weight of a tin of tea. 2T = 520 3

∴ A tin of tea weighs grams.

Checking: A tin of tea weighs grams.

2 tin of tea weighs grams. 3

There is a discount of 15% of water colour in a stationery shop. A box of water colour costs 102 dollars now. Find its original price.

Let S dollars be the original price of the box of water colour. S × (1 – 15%) = 102 = = S =

∴ The original price is dollars.

Checking: The original price of the box of water colour is dollars.

It costs dollars now. 271: Solve the problem by writing an equation.

3 Peter bought a digital camera with of his savings. He remained 3350 8 dollars. What were the original savings of Peter?

Let M dollars be the original savings of Peter.

∴ The original savings of Peter were dollars.

Checking: Peter had dollars originally.

3 He spent of his savings, that is dollars. 8

He remained dollars.

272: Solve the problem by writing an equation. There is a bag of candies. 58% of them are juicy candies and 42% of them are milk candies. There are 8 more juicy candies than milk candies. How many candies are there in the bag altogether?

Let Q be the number of candies in the bag.

∴ There are candies in the bag.

Checking: There are candies in the bag. = . 58% of them are juicy candies, that is juicy candies. = . 42% of them are milk candies, that is pieces. = . There are more juicy candies than milk candies.

1 1 There was a pot of tea. Cindy drank of it and Mandy drank of it. 5 6 Cindy drank 35 mL more than Mandy. How many millilitres of tea in the pot originally?

Let L mL be the original amount of tea in the pot.

∴ There were mL of tea in the pot originally.

Checking: There were mL of tea in the pot originally.

1 Cindy drank of it, that is mL. 5

1 Mandy drank of it, that is mL. 6 = . Cindy drank mL more than Mandy.

After drinking 270 mL of juice from a bottle, Mary pours the remaining juice into 4 glasses equally. Each glass contains 315 mL. How much juice did the bottle contain originally?

Let y mL be the original amount of juice in the bottle. y – 270 = 315 4

∴ The bottle contained mL of juice originally.

Checking: The bottle contained mL of juice originally. = . After drinking 270 mL of juice, there are mL of juice left. The rest is poured into 4 glasses equally. = . Each glass contains mL of juice.

There are 61 lilies in a floral shop. The number of lilies is 30 fewer than 7 of that of carnations. How many carnations are there? 9

Let Q be the number of carnations in the floral shop. 7Q – 30 = 61 9

∴ There are carnations in the floral shop.

Checking: There are carnations in the floral shop. 7 The number of lilies is 30 fewer than of that of carnations. 9

There are lilies in the floral shop.

The base of an isosceles triangle is 6.2 cm. Its perimeter is 22.6 cm. What is the length of each of the two equal sides?

H cm H cm

6.2 cm Let H cm be the length of each of the two equal sides. 2H + 6.2 = 22.6

 The length of each of the two equal sides is cm.

Checking: The lengths of the sides of the triangle are cm, cm and cm.

The perimeter of the triangle is cm.

The length of the lower base and the height of a trapezium are 11 cm and 7 cm respectively. Its area is 56 cm2. What is the length of its upper base? L cm

11 cm Let L centimetres be the length of the upper base of the trapezium.

 The length of the upper base is cm.

Checking:

Area of a trapezium =

In a book store, 28% of the magazines were sold in the morning. In the afternoon, 37% of the magazines were sold. Finally, 105 magazines were left. How many magazines were in the book store originally?

Let M be the number of magazines in the book store originally.

 There were magazines in the book store originally.

Checking: There were magazines originally. In the morning, 28% of them were sold. = magazines were sold in the morning. In the afternoon, 37% of them were sold. = magazines were sold in the afternoon. = magazines were left finally. 405： Solve the problem by writing an equation.

(a) There are 50 apples in half of a box. How many apples are there in a box? Let x be the number of apples in a box. x = 50

x × = 50 ×

 There are apples in a box. 3 (b) There are 21 oranges in of a box. How many oranges are there in 16 a box? Let y be the number of oranges in a box.

 There are oranges in a box.

408： Solve the problem by writing an equation.

Mother is 40 years old. Her age is 5 times that of Chris. What is the age of Chris?

Let m be the age of Chris.

 Chris is years old.

409 Solve the problem by writing an equation.

Chris is 160.2 cm tall and his father is 182 cm tall. The difference of the 1 heights between Chris and his father is of the height of his grandfather. 8 Find the height of his grandfather.

Let h cm be the height of his grandfather.

 His grandfather is cm tall.

Harry bought half of a dozen of ball pens. He paid 50 dollars and got a change of 17.6 dollars. What is the price of each ball pen?

Let P dollars be the price of each ball pen. P = –

 The price of each ball pen is dollars. 412： Solve the problem by writing an equation.

1 There is a box of cookies. Maggie and Michael ate 40% and of the 4 whole box respectively. They ate 26 cookies altogether. How many cookies in the box originally?

In class 6B, the number of girls is 2 times of the number of boys. There are 39 pupils in the class. How many boys in the class?

A box of washing powder costs 28 dollars. A packet of chips costs 3.5 dollars. Mother bought a box of washing powder and several packets of chips and they cost altogether 52.5 dollars. How many packets of chips did mother buy?

415： Solve the problems by writing equations.

Trapezium ABCD is shown as below.

D a m C

h m A B 16 m E 8 m

(a) The area of the triangle EBC is 28 m2. What is the height of the trapezium?

 The height of the trapezium is m.

Checking: Base  Height Area of a triangle = 2 =

(b) The area of the trapezium ABCD is 119 m2. What is the length of the upper base of the trapezium? Let a metres be the length of the upper base of the trapezium.

 The length of the upper base is m.

Checking: Area of a trapezium = =