13) What number should be added to each of the numbers 3,5,13 and 19 so that the resulting numbers may be in proportion?
Answers
Answer:
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Step-by-step explanation:
Let the number be x
I suppose that the meaning of the question could be explained by this equation.
3+x5+x=13+x19+x
By doing criss-cross
(3+x)×(19+x)=(5+x)×(13+x)
57+22x+x2=65+18x+x2
Get the like terms together
22x−18x+x2−x2=65–57
Simplify
4x=8
x=2
Let's check our answer.
3+2=5 5+2=7 13+2=15 19+2=21
15/21 = 5/7
The answer is 2
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Suppose you add x to the four numbers.
(3+x):(5+x) = (13+x):(19+x). Thus
(3+x)(19+x) =(5+x)(13+x)
57 + 22x + x^2 = 65 +18x + x^2, or
4x = 8, or x = 2
Answer is 2.
Check : (3+x):(5+x) = (13+x):(19+x) becomes
5:7 = 15:21 or
5*21 = 7*15 = 105. Correct.
《2,5,2,1》
5,10,15,20