Question

The sum of two numbers is 97. The larger number is three less than four times the smaller number. Find the numbers.

Answer 1

Step-by-step explanation:

Answer:-

Given that:-

• Sum of two numbers is 97.
• The larger number 3 times less than 4 times smaller number.

Concept:-

Step by step formation of the equation:-

• So, let the number be $\sf{x}$
• Larger number is $\sf{4x-3}$

Let's Do!

$\sf{x+ 4x-3=97}$

$\sf{x+ 4x- 3=97}$

$\sf{5x=97+3}$

$\sf{5x= 100}$

$\sf{x= \dfrac{100}{5}}$

$\sf{x= 20}$

So, $\sf{x= 20}$ is the smaller number.

What about the larger one??

Simple, placement of x in the equation.

$\sf{4x-3}$

= $\sf{4(20)-3}$ [Breaking down of Brackets]

= $\sf{80-3 }$

= $\sf{77}$

= $\sf{77}$ is the second number.

Answer 2

Step-by-step explanation:

$\sf \underline{Given} :$

• The sum of two numbers is 97.

• The larger number is three less than four times the smaller number.

$\sf \underline{To \: Find} :$

• Find the numbers.

$\sf \underline{Solution \: } :$

.

Let the number is x

Larger number is 4(x - 3)

$\underline{ \boldsymbol{According \: to \: the \: question\: }} : \:$

$\sf \leadsto \: 4x - 3 + x = 97 \\ \\ \sf \: \leadsto \: 5x = 97 + 3 \\ \\ \sf \leadsto \: 5x = 100 \\ \\ \sf \leadsto \: x = \cancel{\frac{100}{5} } \\ \\ \sf \leadsto \: x \: = 20$

Substitute the value of x :

$\sf \leadsto \: large \: number = 4(20)-3 \\ \\ \sf \: \leadsto \: large \: number = 80 - 3 \\ \\ \sf \: \leadsto \: large \: number = \underline{77}$

$\sf \underline{Verification} :$

$\sf \: 20+77= 97 \: proved$