Problem 1
A book has 240 pages. Lena read three fifths of the book on the first day and 18 more pages on the second day. How many pages are left?
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Problem 2
Seven twelfths of a number equal 84. What is the number?
Problem 3
Three segments have lengths in the ratio 3:4:5, and their total length is 144 centimeters. What is the length of the longest segment?
Problem 4
A price of 800 rubles was increased by 15 percent, then the new price was reduced by 10 percent. What is the final price in rubles?
Problem 5
Five containers have an average mass of 42 kilograms. Four containers together weigh 158 kilograms. How many kilograms does the fifth container weigh?
Problem 6
A number was multiplied by 4, then 18 was subtracted from the result. The result was 70. What was the original number?
Problem 7
Using the digits 1, 2, 3, and 4, four-digit even numbers are formed without repeating a digit. How many numbers are possible?
Problem 8
There are 12 participants at a meeting. Each person shakes hands with every other participant exactly once. How many handshakes occur?
Problem 9
A triangle has a base of 18 centimeters and a height of 14 centimeters to that base. What is the area of the triangle?
Problem 10
A rectangular box is 8 decimeters long, 5 decimeters wide, and 3 decimeters high. What is its total surface area?
Answer key and solutions
Problem 1. Answer: 78
On the first day Lena read 240 × 3 ÷ 5 = 144 pages. After 18 more pages, 240 − 144 − 18 = 78 pages remain.
Problem 2. Answer: 144
One twelfth is 84 ÷ 7 = 12. The whole number has 12 such parts: 12 × 12 = 144.
Problem 3. Answer: 60
There are 3 + 4 + 5 = 12 equal parts. One part is 144 ÷ 12 = 12 centimeters, so the longest segment is 5 × 12 = 60 centimeters.
Problem 4. Answer: 828
After the increase, the price was 800 × 115 ÷ 100 = 920 rubles. After the reduction, it became 920 × 90 ÷ 100 = 828 rubles.
Problem 5. Answer: 52
The total mass of the five containers is 42 × 5 = 210 kilograms. The fifth weighs 210 − 158 = 52 kilograms.
Problem 6. Answer: 22
Reverse the operations: 70 + 18 = 88, then 88 ÷ 4 = 22.
Problem 7. Answer: 12
The last digit must be 2 or 4, giving 2 choices. The other three digits can be arranged in 3 × 2 × 1 ways. The total is 2 × 6 = 12 numbers.
Problem 8. Answer: 66
Each of the 12 participants is paired with 11 others, but every handshake is counted twice. Therefore, 12 × 11 ÷ 2 = 66.
Problem 9. Answer: 126
The area of a triangle is half the product of its base and height: 18 × 14 ÷ 2 = 126 square centimeters.
Problem 10. Answer: 158
There are two faces of each size. The area is 2 × (8 × 5 + 8 × 3 + 5 × 3) = 158 square decimeters.