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Soloha48 [4]
2 years ago
11

The difference of 2 squared numbers equals 53, what are the numbers​

Mathematics
1 answer:
Eva8 [605]2 years ago
8 0

Answer:

  27, 26

Step-by-step explanation:

  27^2 -26^2 = 729 -676 = 53

If the numbers are integers, they must differ by an odd number. For some odd number k, we will have ...

  (x +k)^2 -x^2 = 53

  2xk +k^2 = 53

  x = (53 -k^2)/(2k)

  x = 53/(2k) -k/2

The second term is an odd multiple of 1/2. The first term will be an odd multiple of 1/2 only for k=1. For k = 1, we have ...

  x = (53 -1)/2 = 26

The two numbers are 26 and 27.

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You invested 11000 in in 2st fund and 9000 in 2nd fund

<h3><u>Solution:</u></h3>

Given that, You invested money in two funds.  

Last year, the first fund paid a dividend of 8% and the second a dividend of 5%, and you received a total of $1330.  

This year, the first fund paid a 12% dividend and the second only 2%, and you received a total of $1500.

Let the amount in Fund I be $x and amount in Fund II be $ y

Then, for last year ⇒ 0.08x+0.05y=1330 ----- eqn (1)  

And for this year ⇒ 0.12x+0.02y=1500 ------- eqn (2)  

Multiply (1) by 2 ⇒ 0.16 x + 0.1 y = 2660  

Multiply (2) by 5 ⇒ 0.6 x + 0.1 y = 7500

Subtract the two equations  

(2) ⇒ 0.6x + 0.1y = 7500

(1) ⇒ 0.16x + 0.1y = 2660

(-) --------------------------------

0.44x + 0 = 4840

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Now, from eqn (2)  

0.12(11000) + 0.02y = 1500  

0.02y = 1500 – 1320  

0.02y = 180  

y = 9000

Hence, he invested 11000 in in 2st fund and 9000 in 2nd fund

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