Question-190140

Question Number 190140 by otchereabdullai last updated on 28/Mar/23

Commented by Frix last updated on 28/Mar/23

The text is strange anyway. “...the number is increased by 8 and then divided by the sum of the digits” would mean the sum of the digits after adding 8. But then we get no reasonable result.

$$\mathrm{The}\:\mathrm{text}\:\mathrm{is}\:\mathrm{strange}\:\mathrm{anyway}.\:“…\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{is}\:\mathrm{increased}\:\mathrm{by}\:\mathrm{8}\:\mathrm{and}\:\mathrm{then}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}''\:\mathrm{would}\:\mathrm{mean}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:{after}\:\mathrm{adding}\:\mathrm{8}.\:\mathrm{But}\:\mathrm{then}\:\mathrm{we} \\ $$$$\mathrm{get}\:\mathrm{no}\:\mathrm{reasonable}\:\mathrm{result}. \\ $$

Answered by Frix last updated on 28/Mar/23

((10x+(x−1)+8)/(x+(x−1)))=8 ((11x+7)/(2x−1))=8 11x+7=16x−8 5x=15 x=3 The number is 32

$$\frac{\mathrm{10}{x}+\left({x}−\mathrm{1}\right)+\mathrm{8}}{{x}+\left({x}−\mathrm{1}\right)}=\mathrm{8} \\ $$$$\frac{\mathrm{11}{x}+\mathrm{7}}{\mathrm{2}{x}−\mathrm{1}}=\mathrm{8} \\ $$$$\mathrm{11}{x}+\mathrm{7}=\mathrm{16}{x}−\mathrm{8} \\ $$$$\mathrm{5}{x}=\mathrm{15} \\ $$$${x}=\mathrm{3} \\ $$$$\mathrm{The}\:\mathrm{number}\:\mathrm{is}\:\mathrm{32} \\ $$

Commented by otchereabdullai last updated on 28/Mar/23

please the question says find the two numbers so why the 32?

$${please}\:{the}\:{question}\:{says}\:{find}\:{the}\: \\ $$$${two}\:{numbers}\:{so}\:{why}\:{the}\:\mathrm{32}? \\ $$

Commented by JDamian last updated on 28/Mar/23

what two numbers? The text talks about a "two digit number", not numbers.

Commented by mr W last updated on 28/Mar/23

$${usually}\:{it}'{s}\:{s}\:{problem}\:{of}\:{the}\: \\ $$$${translation}.\:{i}\:{think}\:{the}\:{question}\:{is} \\ $$$$“{find}\:{the}\:{two}\:{digits}''.\:{in}\:{many} \\ $$$${languages}\:“{number}''\:{and}\:“{digit}''\:{are} \\ $$$${the}\:{same}\:{word}. \\ $$

Commented by otchereabdullai last updated on 28/Mar/23

$${thanks}\:{a}\:{lot} \\ $$

Answered by manxsol last updated on 29/Mar/23

ab^(−) b<a ((ab^(−) +8)/(a+b))=8 10a+b+8=8a+8b 2a+8=7b a+4=((7b)/2) a=((7b)/2)−4 (((7b)/2)−4)b^(−) ={32}

$$\overline {{ab}}\:\:\:\:\:\:\:{b}<{a} \\ $$$$\frac{\overline {{ab}}+\mathrm{8}}{{a}+{b}}=\mathrm{8} \\ $$$$\mathrm{10}{a}+{b}+\mathrm{8}=\mathrm{8}{a}+\mathrm{8}{b} \\ $$$$\mathrm{2}{a}+\mathrm{8}=\mathrm{7}{b} \\ $$$${a}+\mathrm{4}=\frac{\mathrm{7}{b}}{\mathrm{2}} \\ $$$${a}=\frac{\mathrm{7}{b}}{\mathrm{2}}−\mathrm{4} \\ $$$$\left(\overline {\frac{\mathrm{7}{b}}{\mathrm{2}}−\mathrm{4}\right){b}}=\left\{\mathrm{32}\right\} \\ $$

Commented by otchereabdullai last updated on 29/Mar/23

$${thanks}\:{sir}! \\ $$

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