Question

the sum of two numbers is 21.five times the first number added to 2 times the second number is 66.find the number

Answer 1

Answer:

the numbers are 8 and 31

Step-by-step explanation:

let the first number he' x' and the the second number be 'y'

By the first Condition:-

x+y=21___________(1)

by the second condition:-

5x+2y=66__________(2)

multiply equation (1) by '2'

therefore,

2x+2y=42_______(3)

subtracting equation (3)from(2)

5x+2y=66__________(2)

2x+2y=42_______(3)

___________

3x=24

therefore x=24/3 i.e

x=8

put x=8 in equation (1)

x+y=21

8+y=21

y=21-8

y=13

therefore the numbers are 8 and13

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Answer 2

$\mathfrak{\large{\underline{\underline{Answer}}}}$

The Numbers are 8 and 13.

$\mathfrak{\large{\underline{\underline{Step-by-step\: Explanation}}}}$

Given :

Sum of the numbers = 21

5 times the first number added to 2 times the second number = 66

To find :

The Numbers

Solution :

$\textbf{\small{\underline{Let the Numbers be as -}}}$

• One as x
• Second as (21 - x)

$\textbf{\small{\underline{According to the Question - }}}$

5 times the first number added to 2 times the second number = 66

★ $\green{\boxed{\green{\boxed{\red{\sf{5x + 2(21 - x) = 66}}}}}}$

$\sf{\implies} \: 5x + 2(21 - x) = 66 \\ \\ \sf{\implies} \: 5x + 42 - 2x = 66 \\ \\ \sf{\implies} \: 3x + 42 = 66 \\ \\ \sf{\implies} \: 3x = 66 - 42 \\ \\ \sf{\implies} \: 3x = 24 \\ \\ \sf{\implies} \: x = \frac{24}{3} \\ \\ \sf{\implies} \: x = 8$

One Number = 8

$\rule{300}{1.5}$

★ Value of (21 - x)

$\sf{\implies} \: 21 - 8 \\ \sf{\implies} \: 13$

Second Number = 13

$\therefore$ The Numbers are 8 and 13.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

Check whether 8 and 13's sum is 21 or not.

$\sf{\implies} \: 8 + 13 = 21 \\ \sf{\implies} \: 21 = 21 \\ \sf{\implies} \: LHS = RHS$

Place the value of x in the equation and check whether both the sides are equal.

$\sf{\implies} \: 5(8) + 2(21 - 8) = 66 \\ \sf{\implies} \: 40 + 42 - 16 = 66 \\ \sf{\implies} \: 82 - 16 = 66 \\ \sf{\implies} \: 66 = 66 \\ \sf{\implies} \:LHS = RHS$

$\therefore$ The Numbers are 8 and 13.