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24. Two numbers are i added tonumber, the ratio becomes 7: 8. Find the numbers.(Ans. 10 and 14]5 If 10 be added to each number |
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Answer» Answer: Step-by-step EXPLANATION: When 1 is added to each of the given two numbers, their ratio becomes 3:4 and when 5 is subtracted from each, the ratio becomes 7:10. What are the numbers? 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 . |
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