Question

Sophia is younger than Mohal. Their ages are consecutive odd integers. Find Sophia's age if the product of their ages is 15.

Answer 1

`3`

Explanation:

`\mathrm{Let\ the\ age\ of\ Sophia\ be\ }x\mathrm{\ and\ age\ of\ Mohal\ be\ }x+2.\\\mathrm{Given,}\\\mathrm{Product\ of\ their\ ages = 15}\\\mathrm{or,\ }x(x+2)=15\\\mathrm{or,\ }x^2+2x=15\\\mathrm{or,\ }x^2+2x-15=0\\\mathrm{or,\ }x^2+5x-3x-15=0\\\mathrm{or,\ }x(x+5)-3(x+5)=0\\\mathrm{or,\ }(x+5)(x-3)=0\\\mathrm{i.e.}\ x=-5\ \mathrm{or}\ 3.`

`x=-5\ \mathrm{is\ disgarded\ because\ age\ cannot\ be\ negative.}\\\mathrm{So\ the\ age\ of\ Shopia,\ }x=3`