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The sum of two numbers is 100 and their difference is 37. The differen [#permalink]
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Question Stats: Hide Show timer StatisticsThe sum of two numbers is 100 and their difference is 37. The difference of their squares is:(A) 37(B) 63(C) 100(D) 3700 (E) 4700 _________________
Re: The sum of two numbers is 100 and their difference is 37. The differen [#permalink]
Bunuel wrote: The sum of two numbers is 100 and their difference is 37. The difference of their squares is:(A) 37(B) 63(C) 100(D) 3700 (E) 4700 Given: \(x + y = 100\)\(x - y = 37\)To find:\(x^2 - y^2 = ?\)From the given info, add both:\(2x = 137\)\(x = \frac{137}{2}\)\(Then, y = \frac{63}{2}\)\(x^2 - y^2 =\frac{137^2}{2^2} - \frac{63^2}{2^2}\)= \(\frac{1}{4} (137^2 - 63^2)\)= \(\frac{1}{4} (137 + 63)(137 - 63)\)= \(\frac{1}{4} (200)(74)\)= 50 x 74= 3700Option D
The sum of two numbers is 100 and their difference is 37. The differen [#permalink] IMO Da+b=100and a-b=37we know,\((a+b)(a-b)=a^2-b^2\) =>\(a^2-b^2= 37*100=3700\)
Re: The sum of two numbers is 100 and their difference is 37. The differen [#permalink]
Nefertiti9 wrote: IMO Da+b=100and a-b=37we know,\((a+b)(a-b)=a^2-b^2\) =>\(a^2-b^2= 37*100=3700\) Easier and time saving!
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Re: The sum of two numbers is 100 and their difference is 37. The differen [#permalink]
Bunuel wrote: The sum of two numbers is 100 and their difference is 37. The difference of their squares is:(A) 37(B) 63(C) 100(D) 3700 (E) 4700 \(a + b = 100\) ; \(a - b = 37\)We know, \(a^2 - b^2 = (a + b)(a - b)\)Thus, \(a^2 - b^2 = 100*37 => 3700\), Answer will be (D) _________________
Re: The sum of two numbers is 100 and their difference is 37. The differen [#permalink] 09 May 2022, 09:31
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Let the numbers be a and b.Then, a + b = 100 and a - b = 37 ∴ a2 - b2 = (a+b) (a-b) = 100 x 37= 3700
Akbar D. the sum of two numbers is 100 and their difference is 37. the differnece of their squares is? 2 Answers By Expert Tutors
Carol H. answered • 08/23/17 Masters' Degree in Mathematics with 35 Years of Teaching Experience
Let x = the larger number Let y = the smaller number x-y = 37 Add these two equations together. (137/2)2 - (63/2)2 = 3700
If the numbers are x and y, then (x+y)(x-y) = x2 - y2 [use F-O-I-L to verify this] So, (100)(37) = 3700 [note: we do not need to find the values of x and y] |