i. A child places 0 or more pennies in her piggy bank each day, for 15 consecutive days. She then cracks open the piggy bank and finds that she has accumulated one dollar. (1 dollar = 100 pennies.) Explain how we know that on at least two days she placed the same number of pennies in her piggy bank. ii. Five friends are at a party. Show that at least two people shook the same number of hands. iii. An equilateral triangle measures 3 centimeters on each side contains 100 dots at random locations. Show that no matter how the dots are distributed, it is always possible to cover 12 or more dots with an equilateral triangle measuring 1 centimeter on each side. We need to a proof for each of these
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
i. A child places 0 or more pennies in her piggy bank each day, for 15 consecutive days. She then cracks open the piggy bank and finds that she has accumulated one dollar. (1 dollar = 100 pennies.) Explain how we know that on at least two days she placed the same number of pennies in her piggy bank.
ii. Five friends are at a party. Show that at least two people shook the same number of hands.
iii. An equilateral triangle measures 3 centimeters on each side contains 100 dots at random locations. Show that no matter how the dots are distributed, it is always possible to cover 12 or more dots with an equilateral triangle measuring 1 centimeter on each side.
We need to a proof for each of these
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