Question

Construct a word problem on simultaneous linear equations in two variables
( on age,rupees, metres, speed, etc.), so that the value of one variable will be 18.
(OEQ)
​

Answer 1

Hi, thanks for this question! :)

To solve such kind of question, the only thing you must know is addition, subtraction (most of the questions can be formed using just these two operation) multiplication and division (there's very rare case where we tend to use these operation).

★ Word Problem :

• $\bold{\tt{\blue{The\: length\: of \:a\: rectangular}}}$

$\bold{\tt{\red{plot\: is \:15 \:cm\: more\: than \:the\:breadth}}}$

$\bold{\tt{\blue{Solve\:for\:the\:breadth\:if\:the\:perimeter}}}$

$\bold{\tt{\red{of\:the\:plot\:is\:42\:cm.}}}$

Let's solve the word problem.

Given :

• Length of the plot is 15 cm more than the breadth.
• Perimeter of the rectangular plot is 42 cm.

To Find :

• Length of the rectangular plot.

Solution :

Let the breadth of the rectangular plot be y cm.

Let the length of the rectangular plot be x cm.

$\sf{\underline{\underline{As\:per\:the\:first\:condition:}}}$

→ $\tt{x=y+15}$

→ $\tt{x-y=15\:\:\:(i)}$

$\sf{\underline{\underline{As\:per\:the\:second\:condition:}}}$

→ $\tt{42\:=\:2\:(x+y)}$

→ $\tt{\dfrac{42}{2}\:=\:x+y}$

→ $\tt{21=x+y\:\:\:(ii)}$

★ Solve equation (ii) and (ii) simultaneously.

Add equation (ii) to (i),

→ $\tt{x-y\:+\:x+y\:=\:21\:+\:15}$

→ $\tt{2x=36}$

→ $\tt{x\:=\:{\dfrac{36}{2}}}$

→ $\tt{x\:=\:18}$

★ Substitute x = 18 in equation (i)

→ $\tt{x-y=15}$

→ $\tt{18-y=15}$

→ $\tt{-y=15-18}$

→ $\tt{-y=-3}$

→ $\tt{y=3}$

$\bold{\large{\boxed{\sf{\red{Length\:of\:the\:rectangular\:plot\:=\:x\:=\:18\:cm}}}}}$

$\bold{\large{\boxed{\sf{\blue{Breadth\:of\:the\:rectangular\:plot\:=\:y\:=\:3\:cm}}}}}$

#Shinchan_Lover  ❤️

$\bold{\large{\boxed{\purple{\tt{I\:Love\:You\:,\:Dipali\:Dii!}}}}}$