Question

8. When one is added to each of two given numbers, their ratio becomes 3 : 4 and when 5 is subtracted
from each, the ratio becomes 7:10, the numbers are:
(8, 11/11, 15/26, 35/27, 36)
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Answer 1

Answer:

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Step-by-step explanation:

Call the numbers  a  and  b , we know:

a+1b+1=34  

a−5b−5=710  

Transforming 2. to  a :

a−5b−5=710∣10(b−5)  

10(a−5)=7(b−5)∣ extend  

10a−50=7b−35∣+50  

10a=7b+15∣÷10  

a=7b10+32  

Putting into 1.:

a+1b+1=34∣a=7b10+32  

(7b10+32)+1b+1=34∣32+1=52  

7b10+52b+1=34∣7b10+52=7b+2510  

7b+2510b+1=34∣b+1=b+11  

7b+2510b+11=34∣αβγδ=αβ×δγ=αδβγ  

7b+2510(b+1)=34∣×40(b+1)  

4(7b+25)=30(b+1)∣ extend  

28b+100=30b+30∣−28b−30,⟺  

2b=70∣÷2  

b=35  

a=7⋅3510+32=24510+32=492+32=49+32=522=26  

The numbers are  26  and  35 .

Answer 2

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