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| Temperature Travail II (Posted on 2021-12-25) |
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Determine all possible pairs (x,p) of nonzero integers satisfying this relationship.
(p*x)o Celsius = (p*x2)o Fahrenheit
Provide valid reasoning for your answer.
** It may be noted that F = (9/5)*C +32, where C and F respectively denotes degree(s) Celsius and degree(s) Fahrenheit.
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Submitted by K Sengupta
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Rating: 4.0000 (1 votes)
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Solution:
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(x,p)=(1,-40), (2,80), and (5,2) constitutes all possible solutions to the puzzle under reference.
Explanation:
By the given conditions of the problem, we have:
p*x2 = (9*p*x)/5 +32
=> 5px2 = 9px +160
=> px(5px-9) =160
Accordingly, each of x and 5x-9 must divide 160
Now, nonzero divisors of 160 are:
+/-1, +/-2, +/-4, +/-5, +/-8, +/-10, +/-16, +/-20, +/-32, +/-40, +/-80, and +/-160
Substituting each of these values for x, we observe that (5x-9) divides 160 only when:
x=1, giving: 5x-9=-4, so that: p=(160)/{(1)*(-4)}=-40
x=2, giving: 5x-9=1, so that: p= (160)/(2*1)= 80
x=5, giving: 5x-9=16, so that: p=(160)/(5*16)=2
Consequently, (x,p) = (1,-40), (2,80), and (5,2) constitute all possible pairs in consonance with the given conditions.
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