Question

four times a number and 3 times another number added give 29. Two times the first number and 6 times the second number added gives 28. Find the number.​

Answer 1

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

Let assume that

↝ First number is x

and

↝ Second number is y.

According to statement

↝ Four times a number and 3 times another number added give 29.

$\rm :\longmapsto\:\boxed{ \tt{ \: 4x + 3y = 29 \: }} - - - (1)$

According to statement again,

↝ Two times the first number and 6 times the second number added gives 28.

$\rm :\longmapsto\:2x + 6y = 28$

can be rewritten as

$\rm :\longmapsto\:2(x + 3y)= 28$

$\rm :\longmapsto\:\boxed{ \tt{ \: x + 3y = 14 \: }} - - - (2)$

On Subtracting equation (2) from equation (1), we get

$\rm :\longmapsto\:4x + 3y - x - 3y = 29 - 14$

$\rm :\longmapsto\:3x = 15$

$\bf\implies \:x = 5$

On substituting x = 5, in equation (2), we get

$\rm :\longmapsto\:5 + 3y = 14$

$\rm :\longmapsto\:3y = 14 - 5$

$\rm :\longmapsto\:3y = 9$

$\bf\implies \:y = 3$

Hence,

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{First \: number, \: x = 5} \\ \\ &\sf{Second \: number, \: y = 3} \end{cases}\end{gathered}\end{gathered}$

Verification

Numbers are

$\red{\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{First \: number, \: x = 5} \\ \\ &\sf{Second \: number, \: y = 3} \end{cases}\end{gathered}\end{gathered}}$

Condition :- 1

↝ Four times a number and 3 times another number added give 29.

$\rm :\longmapsto\:4 \times 5 + 3 \times 3 = 20 + 9 = 29$

Hence, Verified

Condition:- 2

↝ Two times the first number and 6 times the second number added gives 28

$\rm :\longmapsto\:2 \times 5 + 6 \times 3 = 10 + 18 = 28$

Hence, Verified

Answer 2

Answer:

x=5 y=3

Step-by-step explanation:

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