High School

1. A car travels 693 km in 7 hours. What is the speed of the car per hour? Write your answer in km/h.

2. The total mass of 14 bags of cement is 588 kg. What is the mass of each bag?

3. Lillian collects stamps and sticks them into a scrapbook. She has 800 stamps and sticks 32 on each page. How many pages of her scrapbook will she use?

4. A builder mixes 4 kg of gravel with 1 kg of cement. How many kilograms of cement must he put into the cement mixer together with 156 kg of gravel?

Answer :

Let's solve each of the problems step-by-step:

  1. Finding the Speed of the Car:

    • To find the speed of the car, divide the total distance traveled by the total time taken.
    • Distance = 693 km, Time = 7 hours.
    • Speed = [tex]\frac{693 \text{ km}}{7 \text{ hours}} = 99 \text{ km/h}[/tex].
    • Thus, the speed of the car is 99 km/h.
  2. Finding the Mass of Each Bag of Cement:

    • To find the mass of each bag, divide the total mass by the number of bags.
    • Total mass = 588 kg, Number of bags = 14.
    • Mass per bag = [tex]\frac{588 \text{ kg}}{14} = 42 \text{ kg}[/tex].
    • Therefore, each bag of cement weighs 42 kg.
  3. Finding the Number of Pages Used in the Scrapbook:

    • To find out how many pages Lillian will use, divide the total number of stamps by the number of stamps per page.
    • Total stamps = 800, Stamps per page = 32.
    • Number of pages = [tex]\frac{800}{32} = 25[/tex].
    • Hence, Lillian will use 25 pages of her scrapbook.
  4. Finding the Amount of Cement Needed:

    • The builder mixes 4 kg of gravel with 1 kg of cement.
    • For every 4 kg of gravel, 1 kg of cement is needed.
    • Given 156 kg of gravel, we find the amount of cement by setting up a proportion:
    • [tex]\frac{4 \text{ kg (gravel)}}{1 \text{ kg (cement)}} = \frac{156 \text{ kg (gravel)}}{x \text{ kg (cement)}}[/tex].
    • Solving for [tex]x[/tex], we multiply and divide: [tex]x = \frac{156 \times 1}{4} = 39 \text{ kg}[/tex].
    • Therefore, the builder needs to put 39 kg of cement with 156 kg of gravel.