Question

Of two numbers, 4 times the smaller one is less than 3 times the larger one by 5. if the sum of the numbers is larger than 6 times their difference by 6, find the larger number.

Answer 1

Let the two numbers be x(smaller) and y(larger) .

We will have the following equations :

4x = 3y - 5

4x - 3y = - 5

3y - 4x = 5....... 1)

x + y = 6(y - x) + 6

x + y = 6y - 6x + 6

7x - 5y = 6........ 2)

Solving 1 and 2 simultaneously.

Multiply equation 1 by 5 and equation 2 by 3 we get :

15y - 20x = 25

21x - 15y = 18

Adding the two :

x = 43

3y - 4 × 43 = 5

3y - 172 = 5

3y = 177

Y = 177/3

Y = 59

Answer 2

Answer: The smaller number= 45, larger number = 62

Step-by-step explanation:

Let the Smaller number= x

Let the larger Number = y

According to the question,

                                     3y - 4x = 6  ..............................(1)

Also, It is given ,             (x + y) - 6( y - x ) = 5

                                ⇒  x + y -6y + 6x = 5

                                ⇒ - 5y + 7x = 5 ............................(2)

On solving (1) and (2),

⇒( 3y - 4x = 6 )   × 5             ⇒ 15y -20x = 30

 (- 5y + 7x = 5 )  × 3              +(-15y+21x = 15)

                                                            x = 45

Substituting x = 45 in (1)

⇒ 3y - (4 ×45) = 6

⇒3y -180 = 6

⇒3y = 180+ 6

⇒3y= 186

⇒y = 186/3

⇒y= 62

∴ The smaller number= 45, larger number = 62

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