Questions instructional visually solved and created by Chin Pei Yi
Video Scripted by Chin Pei Yi
Jane baked some cookies. She gave 3/5 of the cookies to Amy and 3/4 of the remainder to Bob. Given that she gave 15 more cookies to Amy than Bob, how many cookies did Jane bake at first?
First, we start with the total number of cookies, which is represented as 5 over 5. Amy receives 3 over 5 cookies, leaving us with 2 over 5. Next, we take the remaining 2 over 5 and multiply it by 3 over 4, which is the portion given to Bob. This gives us 6 over 20. We then simplify the fraction by dividing both the numerator and denominator by 2, resulting in 3 over 10. So, Bob receives 3 over 10 of the cookies.
Now, given that Amy has 15 more cookies than Bob, we take Amy's fraction of cookies, 3 over 5, and subtract Bob's fraction, 3 over 10, to find the difference. To make the subtraction easier, we multiply the numerator and denominator of Amy’s fraction by 2, giving us 6 over 10. Subtracting Bob's 3 over 10 from this leaves us with 3 over 10. This means that 3 over 10 of the total cookies is equal to 15.
So, from this, we can determine that Jane originally baked 50 cookies.
Script:
ABCD is a rectangle. DE = EF = FC. The area of triangle AFD to the area of triangle
EOF is 8:1. What is the fraction of the shaded area to the total area of rectangle ABCD?
EOF is 8:1. What is the fraction of the shaded area to the total area of rectangle ABCD?
Given that DE, EF, and FC are equal, we can divide the rectangle ABCD into three equal parts. The area of triangle AFD compared to triangle EOF is in a ratio of 8:1, meaning triangle EOF occupies 1 unit out of the 8 units in triangle AFD. The remaining area of triangle AFD, which is AODE, therefore represents 7 units. Similarly, the opposite side of AODE, triangle BOFC, also consists of 7 units.
Next, by dividing the rectangle ABCD into three equal parts, we can see that the first two columns form a rectangle, which can be split in half. We already know that one half is made up of 7 units and 1 unit, totaling 8 units. This means the other half is also 8 units. Adding the first 8 units to the second 8 units, we get 16 units in total, which represents two-thirds of the rectangle ABCD.
To find the value of one-third, we divide 16 by 2, giving us 8 units. This means that each of the three equal parts of the rectangle ABCD is 8 units. To find the total area of the rectangle, we multiply 8 by 3, giving us 24 units.
Finally, to determine the value of the shaded area, we add the 7 units from AODE, 1 unit from EOF, and 7 units from BOFC, giving us a total of 15 units. Dividing this by the total area of 24 units and simplifying, we get a fraction of 5/8. So, the fraction of the shaded area to the total area of the rectangle ABCD is 5/8.