Question

The sum of two numbers is 72. If twice the smaller is 3 more than the greater,
find them.​

Answer 1

Answer:

X=47, y=25

Step-by-step explanation:

let the numbers he X and y, ATQ stands for according to Question. X>Y

Answer 2

ANSWER :

★ If the sum of two numbers is 72 and twice the smaller is 3 more than the greater, then the numbers are 25 and 47.

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SOLUTION :

❖ Given :-

• Sum of the two numbers is 72

• Twice of the smaller number is 3 more than the greater.

❖ To Find :-

• The numbers = ?

❖ Method 1 :-

Suppose,

• The smaller number = x

• The greater number = y

According to first condition,

$\: \: \: \: \bigstar \: \: \: \sf{ \large{x + y = 72 \: \: - - - - - > (1)}}$

According to second condition,

$\: \: \: \: \bigstar \: \: \: \sf{ \large{2x = y + 3 \: \: - - - - - > (2)}}$

Now,

$\: \: \: \: \: \: \sf{ \large{(1) \implies \: x + y = 72}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \sf{ \large{ \implies \: y = 72 - x \: \: - - - - > (3) }}$

➥ Replacing y from eq. (3) in eq. (2) :-

$\sf{ \large{(2) \implies \: 2x = y + 3}} \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \large{ \implies \: 2x = (72 - x) + 3 }} \\ \\ \: \: \: \: \: \: \: \: \: \sf{ \large{ \implies \: 2x = 72 - x + 3}} \\ \\ \: \: \: \: \: \: \: \: \: \: \sf{ \large{ \implies \: 2x + x = 72 + 3 }} \\ \\ \sf{ \large{ \implies \: 3x = 75}} \: \: \: \: \: \\ \\ \sf{ \large{ \implies \: x = \dfrac{75}{3}}} \: \: \: \: \: \\ \\ \sf{ \large{ \therefore \: \: \underline{ \: x = 25 \: }}}$

➥ Putting the value of x in eq. (3) :-

$\sf{ \large{(3)\implies \: y = 72 - x}} \: \: \\ \\ \: \: \: \: \: \: \: \sf{ \large{\implies \: y = 72 - 25}} \\ \\ \: \: \: \: \: \: \sf{ \large{ \therefore \: \: \underline {\: y = 47 \:}}}$

• The smaller number, x = 25

• The greater number, y = 47

★ Hence, the numbers are : 25 and 47.

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❖ Method 2 :-

Suppose,

• The smaller number = a

According to first condition,

• The greater number = 72 - a

According to second condition,

$\bigstar \: \: \sf{ \large{2a = (72 - a) + 3 \: \: - - - - - > (1)}}$

➥ Solving eq. (1) :-

$\: \: \: \: \sf{ \large{(1) \implies \: 2a = (72 - a) + 3 }} \\ \\ \: \: \: \: \: \: \: \: \: \sf{ \large{ \implies \: 2a = 72 - a + 3}} \\ \\ \: \: \: \: \: \: \: \: \: \: \sf{ \large{ \implies \: 2a + a = 72 + 3 }} \\ \\ \sf{ \large{ \implies \: 3a = 75}} \: \: \: \: \: \\ \\ \sf{ \large{ \implies \: a = \dfrac{75}{3}}} \: \: \: \: \: \\ \\ \sf{ \large{ \therefore \: \: \underline{ \: a = 25 \: }}}$

$\sf{ \large{ \therefore \: \: The \: \: greater \: \: number = 72 - a }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \large{= 72 - 25 }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{\large{= \underline{ \: 47 \: }}}$

• The smaller number = 25

• The greater number = 47

★ Hence, the numbers are : 25 and 47.