Question

Age of remya and double the age of sofi added together gives 28.three fourth of remyas age added to one fourth of sofis age gives 11. Find the age of remya and the age of sofi

Answer 1

$Let \: the \: age \: of \: Remya = x \: years$

$The \: age \: of \: Sofi = y\: years$

/* According to the problem given */

$Age \: of \: Remya \: and \: double \: the \:age\\of \: Sofi \: added \: together \: gives \: 28$

$\implies x + 2y = 28 \\\implies x = 28 - 2y \: ---(1)$

$Three \: fourth \: of \: Remya \: age \: added \\to \: one \: fourth \: of \: Sofis \: age \: gives \: 11$

$\implies \frac{3}{4} x + \frac{1}{4} y = 11$

/* Multiplying bothsides by 4 , we get */

$\implies 3x + y = 44 \: ---(2)$

/* Put x = 28 - 2y in equation (2) , we get */

$\implies 3( 28 - 2y ) + y = 44$

$\implies 84 - 6y + y = 44$

$\implies - 5y = 44 - 84$

$\implies - 5y = - 40$

$\implies y = \frac{ - 40 }{-5}$

$\implies y = 8$

/* Put y = 8 in equation (1), we get */

$x = 28 - 2 \times 8$

$\implies x = 28 - 16$

$\implies x = 12$

Therefore.,

$\red{ The \: age \: of \: Remya }\green {= 12 \: years}$

$\red{The \: age \: of \: Sofi}\green { = 8\: years }$

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Answer 2

Answer:

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➡Let remya age be x and sofia age be y

➡ATQ to 1st statement :-

2y + x = 28 --- ( i )

➡ATQ to 2nd statement

3/4 x + 1/4y = 11

3x + y / 4 = 11

3x + y = 44 ------- ( ii )

➡Multiply eq ( i ) by 3

6y + 3x = 84 ----- ( iii )

➡Subtracting (ii) from( iii)

6y + 3x - 3x - y = 84 - 44

5y = 40

y = 40 / 5

y = 8

y = 8

➡putting value of y in eq (i)

2y + x = 28

2 x 8 + x = 28

16 + x = 28

x = 28 - 16

➡x = 12

Step-by-step explanation:

Hope I help you!!