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Two girls were born to the same mother, on the same day, at the same time, in the same month and year and yet they’re not twins. How can this be?
Answer: They are in a set of triplets.
Solution:
Carl is trying to find solutions to a geometric puzzle. He has a square plot of land that he needs to reserve 1/4 for himself and divide the remaining 3/4 equally and in similar shape, among his 4 children. There are two possible solutions. Can you solve the puzzle?
Answer: Solution #1 - Squares First, Carl divides his as to reserve to himself one-fourth in the form of a square. Then, Carl takes the remaining 3/4 shape and scales it down by 1/4. He then, multiplies the shape into 4 identically shaped pieces, and aranges them so that they fit into the original 3/4 shape. Solution #2 - Rectangles First, create a triangle that is 1/4 the size of the square. Now, with straight lines, create two squares. Proceed to disect the two squares with horizontal lines creating 4 triangles. Then, disect one of the resultuing triangles from each square. The shape of land for each of his four children is divided evenly and is the same shape.
Solution:
Show Answer
Solution #1 – Squares
First, Carl divides his as to reserve to himself one-fourth in the form of a square.
Then, Carl takes the remaining 3/4 shape and scales it down by 1/4. He then, multiplies the shape into 4 identically shaped pieces, and aranges them so that they fit into the original 3/4 shape.
Solution #2 – Rectangles
First, create a triangle that is 1/4 the size of the square.
Now, with straight lines, create two squares.
Proceed to disect the two squares with horizontal lines creating 4 triangles.
Then, disect one of the resultuing triangles from each square. The shape of land for each of his four children is divided evenly and is the same shape.
Show Answer
Solution #1 – Squares
First, Carl divides his as to reserve to himself one-fourth in the form of a square.
First, Carl divides his as to reserve to himself one-fourth in the form of a square.
Then, Carl takes the remaining 3/4 shape and scales it down by 1/4. He then, multiplies the shape into 4 identically shaped pieces, and aranges them so that they fit into the original 3/4 shape.
Solution #2 – Rectangles
First, create a triangle that is 1/4 the size of the square.
Now, with straight lines, create two squares.
Proceed to disect the two squares with horizontal lines creating 4 triangles.
Then, disect one of the resultuing triangles from each square. The shape of land for each of his four children is divided evenly and is the same shape.
David is throwing Robert a surprise birthday party but he has to stay within his budget. He spent half of his money plus $2.00 on the cake. Half of what he had left plus $2.00 was spent on balloons and streamers. Then he spent half of what he had left plus $1.00 on candy. Now he is out of money, how much did he start with?
Answer: This one is best solved working backwards, the last part David spent half of what was left plus $1.00 on candy and then was out of money. That means he must have spent $2.00 on Candy as $1.00 was half of what he had using the same logic backwards: $2.00 on candy $6.00 on Balloons and Streamers $12.00 on the cake Total of $20.00.
Solution:
Show Answer
This one is best solved working backwards, the last part David spent half of what was left plus $1.00 on candy and then was out of money. That means he must have spent $2.00 on Candy as $1.00 was half of what he had using the same logic backwards: $2.00 on candy $6.00 on Balloons and Streamers $12.00 on the cake Total of $20.00.
Show Answer
This one is best solved working backwards, the last part David spent half of what was left plus $1.00 on candy and then was out of money. That means he must have spent $2.00 on Candy as $1.00 was half of what he had using the same logic backwards: $2.00 on candy $6.00 on Balloons and Streamers $12.00 on the cake Total of $20.00.
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