Question

Need an only genuine answer
Amina thinks of consecutive number and multiply it with 2,3,4 and when she add the sum she got is 74 what are her numbers

Answer 1

$\large\underline{\sf{Solution-}}$

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:Let-\begin{cases} &\sf{first \: consecutive \: number = x} \\ &\sf{second \: consecutive \: number = x + 1}\\ &\sf{third \: consecutive \: number = x + 2} \end{cases}\end{gathered}\end{gathered}$

According to statement,

If consecutive numbers are multiplied by 2, 3, 4 respectively and add, we get 74.

$\rm :\longmapsto\:2x + 3(x + 1) + 4(x + 2) = 74$

$\rm :\longmapsto\:2x + 3x + 3 + 4x + 8 = 74$

$\rm :\longmapsto\:9x + 11 = 74$

$\rm :\longmapsto\:9x = 74 - 11$

$\rm :\longmapsto\:9x = 63$

$\rm :\implies\:x = 7$

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:Hence-\begin{cases} &\sf{first \: consecutive \: number = 7} \\ &\sf{second \: consecutive \: number = 8}\\ &\sf{third \: consecutive \: number = 9} \end{cases}\end{gathered}\end{gathered}$

Verification :-

First consecutive number = 7

Second consecutive number = 8

Third consecutive number = 9

So,

2 × 7 + 3 × 8 + 4 × 9

= 14 + 24 + 36

= 74

Hence, Verified

Basic Concept Used :-

Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.