Question

Hamid has three boxes of different fruits. Box A weighs ${\displaystyle 2\frac{1}{2}}$ kg more than Box B and Box C weighs ${\displaystyle 10\frac{1}{4}}$ kg more than Box B. The total weight of the three boxes is ${\displaystyle 48\frac{3}{4}}$ kg. How many kilograms (kg) does Box A weigh?

Answer 1

Let the weight of box A be x kg.

According to the question,

Weight of Box A = Weight of Box B + ${\displaystyle \frac{5}{2}}$ kg  ...[Given]

⇒ Weight of box B = ${\displaystyle (x-\frac{5}{2})}$ kg

And weight of Box C = Weight of box B + ${\displaystyle \frac{41}{4}}$ kg  ...[Given]

⇒ Weight of Box C = ${\displaystyle x-\frac{5}{2}+\frac{41}{4}}$ kg

= ${\displaystyle x+\left(\frac{-10+41}{4}\right)}$ kg

= ${\displaystyle (x+\frac{31}{4})}$ kg

As, total weight of three boxes = ${\displaystyle 48\frac{3}{4}}$ kg = ${\displaystyle \frac{195}{4}}$ kg    ...[Given]

∵ Total weight of three boxes = Weight of box A + Weight of box B + Weight of box C

∴ ${\displaystyle \frac{195}{4}=x+x-\frac{5}{2}+x+\frac{31}{4}}$

⇒ ${\displaystyle \frac{195}{4}=3x+\frac{31-10}{4}}$

⇒ ${\displaystyle \frac{195}{4}=3x+\frac{21}{4}}$

⇒ ${\displaystyle 3x=\frac{195}{4}-\frac{21}{4}}$

⇒ ${\displaystyle 3x=\frac{195-21}{4}}$

⇒ ${\displaystyle 3x=\frac{174}{4}}$

⇒ ${\displaystyle x=\frac{174}{3\times 4}}$

⇒ ${\displaystyle x=\frac{29}{2}}$

∴ ${\displaystyle x=14\frac{1}{2}}$ kg

Hence, box A weight ${\displaystyle 14\frac{1}{2}}$ kg.