Identify the original value and the ratio for increase.

You're on a roll — 13) We can increase or decrease numbers in a given ratio. Increase 690 in the ratio 4:3 Step 1: Identify the original value and the ratio for increase. Original value = 690. Ratio for increase = new partold part = (4)/(3). Step 2: Multiply the original value by the ratio. Increased value = 690 × (4)/(3) Increased value = (690 × 4)/(3) Increased value = (2760)/(3) Increased value = 920 The increased value is 920. 14) In a class of 75 pupils, there are 13 more girls than boys. Find the number of boys in that class. Step 1: Let B be the number of boys and G be the number of girls. We are given two pieces of information: 1. Total pupils: B + G = 75 2. Girls are 13 more than boys: G = B + 13 Step 2: Substitute the second equation into the first equation. B + (B + 13) = 75 2B + 13 = 75 Step 3: Solve for B. 2B = 75 - 13 2B = 62 B = (62)/(2) B = 31 The number of boys in the class is 31. 15) The population of a school increased from 8000 pupils to 10000 pupils. What is the percentage increase? Step 1: Calculate the absolute increase in population. Increase = New population - Old population Increase = 10000 - 8000 = 2000 pupils Step 2: Calculate the percentage increase using the formula: IncreaseOld population × 100\%. Percentage increase = (2000)/(8000) × 100\% Percentage increase = (1)/(4) × 100\% Percentage increase = 25\% The percentage increase is 25\%. 16) The radius of a circle is 14cm. Calculate its perimeter (circumference). Step 1: Recall the formula for the circumference of a circle: C = 2 r. Given radius r = 14 cm. Use = (22)/(7). Step 2: Substitute the values into the formula. C = 2 × (22)/(7) × 14 C = 2 × 22 × (14)/(7) C = 2 × 22 × 2 C = 44 × 2 C = 88 cm The perimeter (circumference) of the circle is 88 cm. 17) When money is borrowed interest is paid. Find the simple interest on 150,000frs for 2 years at 5 (1)/(2)\% Step 1: Identify the principal (P), rate (R), and time (T). P = 150,000 frs R = 5 (1)/(2)\% = 5.5\% T = 2 years Step 2: Use the simple interest formula: I = (P × R × T)/(100). I = (150000 × 5.5 × 2)/(100) I = 1500 × 5.5 × 2 I = 1500 × 11 I = 16500 frs The simple interest is 16,500 frs. 18) 1/2y = 1/4. Calculate the value of y. Step 1: Write the equation. (1)/(2)y = (1)/(4) Step 2: To solve for y, multiply both sides of the equation by 2. 2 × (1)/(2)y = 2 × (1)/(4) y = (2)/(4) y = (1)/(2) The value of y is (1)/(2). 19) The sum of angles of a triangle is 180°. Two angles are 45° and 33° respectively. What is the third angle? Step 1: Let the three angles of the triangle be A, B, and C. We know A + B + C = 180^. Given A = 45^ and B = 33^. Step 2: Substitute the known angles into the sum equation. 45^ + 33^ + C = 180^ 78^ + C = 180^ Step 3: Solve for C. C = 180^ - 78^ C = 102^ The third angle is 102^. 20) What is the place value of 7 in 70465? Step 1: Identify the position of the digit 7 in the number 70465. The number can be broken down by place value: • 5 is in the ones place. • 6 is in the tens place. • 4 is in the hundreds place. • 0 is in the thousands place. • 7 is in the ten thousands place. The place value of 7 in 70465 is Ten Thousands. 21) The distance round a square plot is 240m. How long is each side? Step 1: The distance round a square plot is its perimeter. Perimeter of a square = 4 × side. Given Perimeter = 240 m. Step 2: Set up the equation and solve for the side. 4 × side = 240 side = (240)/(4) side = 60 m Each side of the square plot is 60 m. 22) The average of 3 numbers is 107. What is the sum of the 3 numbers? Step 1: Recall the formula for average: Average = Sum of numbersCount of numbers. Given Average = 107, Count = 3. Step 2: Rearrange the formula to find the sum. Sum of numbers = Average × Count of numbers Sum of numbers = 107 × 3 Sum of numbers = 321 The sum of the 3 numbers is 321. 23) Three tickets for a dance cost 2,400frs. Find the cost of 10 such tickets. Step 1: Find the cost of one ticket. Cost per ticket = Total cost for 3 ticketsNumber of tickets Cost per ticket = 2400 frs3 Cost per ticket = 800 frs Step 2: Calculate the cost of 10 tickets. Cost for 10 tickets = Cost per ticket × 10 Cost for 10 tickets = 800 frs × 10 Cost for 10 tickets = 8000 frs The cost of 10 tickets is 8,000 frs. 24) Find the LCM of 5 and 7. Step 1: Identify the numbers. 5 and 7 are both prime numbers. Step 2: The Least Common Multiple (LCM) of two prime numbers is their product. LCM(5, 7) = 5 × 7 LCM(5, 7) = 35 The LCM of 5 and 7 is 35. 25) Numbers can be added or subtracted. Subtract 3479 from 8001. Step 1: Perform the subtraction. 8001 - 3479 8001 -3479 4522 The result of the subtraction is 4522. 26) Find the average of 3, 4, 5, 6 and 7. Step 1: Sum the numbers. Sum = 3 + 4 + 5 + 6 + 7 = 25 Step 2: Count the number of values. There are 5 numbers. Step 3: Calculate the average: Average = SumCount. Average = (25)/(5) Average = 5 The average of the numbers is 5. 27) Twelve years ago, Blaise was 15 years old. How old is he now? Step 1: To find Blaise's current age, add the number of years that have passed to his age 12 years ago. Current age = Age 12 years ago + 12 years Current age = 15 + 12 Current age = 27 years old Blaise is 27 years old. 28) What distance will a car cover in 20 minutes if it is running at the speed of 75km/hr? Step 1: Identify the speed and time. Speed = 75 km/hr Time = 20 minutes Step 2: Convert the time to hours, as the speed is given in km/hr. 20 minutes = (20)/(60) hours = (1)/(3) hours Step 3: Use the formula Distance = Speed × Time. Distance = 75 km/hr × (1)/(3) hours Distance = (75)/(3) km Distance = 25 km The car will cover a distance of 25 km. 29) The product of a score and a gross divided by a dozen is ____. Step 1: Define the terms: • A score is 20 units. • A gross is 144 units (12 dozen). • A dozen is 12 units. Step 2: Set up the expression based on the problem statement. Product of a score and a gross: 20 × 144. Divided by a dozen: (20 × 144)/(12). Step 3: Perform the calculation. (20 × 144)/(12) = 20 × 1