Question

$\text{John is}3\frac{1}{4}\text{inches taller than William and}\text{William is}2\frac{1}{2}\text{inches shorter than Adam.}\text{If Adam is}70\frac{3}{8}\text{inches tall, find the heights}\text{of John and William.}$

• A. $\text{John :}70\frac{1}{8}\text{in ; William :}67\frac{7}{8}\text{in}$
• B. $\text{John :}71\frac{1}{8}\text{in ; William :}67\frac{7}{8}\text{in}$
• C. $\text{John :}70\frac{1}{8}\text{in ; William :}67\frac{5}{8}\text{in}$
• D. $\text{John :}71\frac{1}{8}\text{in ; William :}67\frac{5}{8}\text{in}$

Answer 1

The correct option is B $\text{John :}71\frac{1}{8}\text{in ; William :}67\frac{7}{8}\text{in}$

$\text{Adam's height}=70\frac{3}{8}\text{inches}$

$\text{William is}2\frac{1}{2}\text{inches}shorter\text{than Adam.}$

$⟹\text{William's height}=(70\frac{3}{8}-2\frac{1}{2})\text{inches}$

$=\frac{(8\times 70)+3}{8}-\frac{(2\times 2)+1}{2}\text{inches}$

$=(\frac{563}{8}-\frac{5}{2})\text{inches}$

$=(\frac{563}{8}-\frac{5\times 4}{2\times 4})\text{inches}$

$=\frac{563}{8}-\frac{20}{8}\text{inches}$

$=\frac{(563-20)}{8}\text{inches}$

$=\frac{543}{8}\text{inches}$

$=67\frac{7}{8}\text{inches}$

$\text{John is}3\frac{1}{4}\text{inches}taller\text{than William.}$

$⟹\text{John's height}$

$=(67\frac{7}{8}+3\frac{1}{4})\text{inches}$

$=(67+3)+(\frac{7}{8}+\frac{1}{4})\text{inches}$

$=70+(\frac{7}{8}+\frac{1\times 2}{4\times 2})\text{inches}$

$=70+(\frac{7}{8}+\frac{2}{8})\text{inches}$

$=70+\frac{(7+2)}{8}\text{inches}$

$=70+\frac{9}{8}\text{inches}$

$=70+1\frac{1}{8}\text{inches}$

$=71\frac{1}{8}\text{inches}$

$\therefore \text{John is}71\frac{1}{8}\text{inches tall and William is}67\frac{7}{8}\text{inches tall.}$