1. some parts are cut out (top right, bottom left) from a rectangle ABCD resulting in the odd shape attached. if the inside area is 110 cm2, find the area of ABCD. see attached doc.
[answer 126]

2. the sum of 4 numbers is 80. if you add 3 to the first number, subtract 3 from the second number, multiply the third number by 3 and divide the fourth number by 3, the result will be equal. what is the difference between the largest and the smallest of the original numbers?
[answer 40]

THANK YOU!

Some parts are cut out (top right, bottom left) from a rectangle ABCD resulting in the odd shape attached. if the inside area is 110 cm2, find the area of ABCD. see attached doc.

For this question you need to recognize that the two cut out areas, while looking the same, form a square as different sides of the 1/4 circle are cut out. I have coloured this in red for better clarity.

While I could solve this with algebra, I feel the level of algebra is beyond the primary school expectations. Thus I shall provide a basic trial & error / guess & check approach.



the sum of 4 numbers is 80. if you add 3 to the first number, subtract 3 from the second number, multiply the third number by 3 and divide the fourth number by 3, the result will be equal. what is the difference between the largest and the smallest of the original numbers?

For this question, I will 'cheat' a little. First you will notice that in the end, all four numbers are the same, so we can work backwards. Also, given one number is increased by 3 and another decreased by 3, then we can basically assume there is no change for either, since we are finding the total value of all 4 numbers, for the purpose of determining the value of 1unit.

A : B : C : D
3 : 3 : 3 : 3
3 : 3 : 1 : 9

16units --> 80
1unit --> 5

When finding the actual value of each of the numbers we need to take into account the increase and decrease of 3 for the first two numbers.

A --> 3units - 3 --> 12
B --> 3units + 3 --> 18
C --> 1unit --> 5
D --> 9units --> 45

Difference between largest and smalest
--> 9units - 1unit
--> 45 - 4 = 40

thanks Chris. for Q2, i'm baffled as to why use 3u as end number for all 4 numbers.

When they say they are the same, I can choose any number I want since we are dealing with units. To make it simple I always start with 1:1:1:1. We see, later in the question, that we need to divide the 3rd number by 3, working backwards, and instead of having 1/3 of a unit, I change the end ratio to 3:3:3:3. This will allow me to have a whole number for the third number.

hmm... ok.