Question

Four times a number and three times another number added together make 43. Two times the second number, subtracted from three times the first gives 11. What are the numbers

Answer 1

$\LARGE{ \underline{\underline{ \sf{Required \: answer:}}}}$

GiveN:

• Four times a number and three times another number added together make 43.

• Two times the second number, subtracted from three times the first gives 11.

To FinD:

• The numbers are?

Step-by-Step Explanation:

Let the first number be x and the second number be y. Then,

According to condition -1)

⇛ 4(First no.) + 3(Second no.) = 43

⇛ 4x + 3y = 43 ---------(1)

According to condition -2)

⇛ 3(First no.) - 2(Second no.) = 11

⇛ 3x - 2y = 11 ---------(2)

To solve using elimination method, let's make the coefficient of one of the variable equal in magnitude.

Multiplying 2 with eq.(1),

⇛ 2(4x + 3y) = 86

⇛ 8x + 6y = 86

Multiplying 3 with eq.(2),

⇛ 9x - 6y = 33

Adding them,

⇛ 17x = 119

⇛ x = 7

Then,

⇛ 4(7) + 3y = 43

⇛ 28 + 3y = 43

⇛ 3y = 15

⇛ y = 5

Hence,

The required values of x and y respectively are:

$\large{ \boxed{ \sf{ \red{7 \: and \: 5}}}}$

Answer 2

Question

Four times a number and three times another number added together make 43. Two times the second number, subtracted from three times the first gives 11. What are the numbers?

Solution

Let, the first number be x

the second number be y

ATP

4x+3y = 43 (i)

3x-2y = 11 (ii)

$(i) \: 4x + 3y = 43 \\ = ) \: 4x = 43 - 3y \\ = ) \: x = \frac{43 - 3y}{4}$

Putting the value of x in equ (ii)

$(ii) \: 3x - 2y = 11 \\ = ) \: 3( \frac{43 - 3y}{4}) - 2y = 11 \\ = ) \: \frac{129 - 9y}{4} - 2y = 11 \\ = ) \: \frac{129 - 9y - 8y}{4} = 11 \\ = ) \: \frac{129 - 17y}{4} = 11 \\ = ) \: 129 - 17y = 11 \times 4 \\ = ) \: 129 - 44 = 17y \\ = ) \: 85 = 17y \\ = ) \: \frac{85}{17} = y \\ = ) \: 5 = y$

Putting the value of y in equ (i)

$(i) \: 4x + 3y = 43 \\ = ) \: 4x + 15 = 43 \\ = ) \: 4x = 43 - 15 \\ = ) \: 4x = 28 \\ = ) \: x = \frac{28}{4} \\ = ) \: x = 7$

Ans:- The value of x is 7.

The value of y is 5.