Mariyam donated some amount to an orphanage from her pocket money. The amount of donation is represented by (a+b) 2 -(a-b) 2 . Her friends wanted to know the amount donated by her. She did not disclose amount but just gave a hint that the value of the expression a+b =209 and a-b=191. Based on this statement answer the following questions:
42. The algebraic identity used to calculate the amount in the situation is_____.
a) (a+b) 2 =a 2 +2ab+b 2 b) a 2 -b 2 =(a+b)(a-b) c) (x+a)(x+b)=x 2 +(a+b)x+a d) (a-b) 2 =a 2 -2ab+b 2
43. The simplified form of (a+b) 2 -(a-b) 2is________.
a) 2ab b) 3ab c) 4ab d) 0
Answers
Answer:
42. (b) a^2-b^2=(a+b)(a-b)
here a=200 and b=9
so, a+b=200+9=209
a-b=200-9=191
43.
(a+b)^2-(a-b)^2
=a^2+2ab+b^2-(a^2-2ab+b^2)
=a^2+2ab+b^2-a^2+2ab-b^2
=4ab
(c) is the correct answer
Answer:
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Some people collected money to be donated in some orphanages. A part of the donation is fixed and the remaining depends on the number of children in the orphanage. If they donated Rs. 9500, in the orphanage having 50 children and Rs. 13,250 with 75 children, find the fixed part of the donation and the amount donated for each child.
What values do these people possess?
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Solution
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Let the fixed donation be Rs.x and amount donated for each child be Rs. y.
Then, According to the question,
x+50y=9500 ....(i)
x+75y=13250....(ii)
Subtrating (i) from (ii) we get
25y=3750 or y=150
From (i) x=9500−50y=9500−50×150=2000
fixed amount donated =Rs.2000
Amount donated for each child =Rs.150
They possess values like Helpfulness, cooperation, happiness, caring.