Question

The sum of two numbers is 80, if the larger number exceeds four times the smaller number by 5 then the smaller number be

Answer 1

The bigger number is 63 and the smaller number is 17.

Step-by-step explanation:

♨ By forming pair of linear equations in two variable

Given, sum of two numbers is 80.

Let the two numbers be x and y respectively.

So, x+y=80 --(1)

Now, the larger number exceeds 4 times the smaller number by 5.

So, let x > y.

So, equation will be

x+5=4y or

x-4y=-5 --(2)

Subtracting eq. (2) by eq. (1)

x-x+y-(-4y)=80-(-5)

5y=85

So, y=17

Putting y=17 in eq. (1)

x+17=80

x=63

Therefore the bigger number is 63 and the smaller number is 17.

Now verifying by putting values of x and y in both the equations

✍ Case 1

(63+17)=80

80=80

So, it's verified.

✍ Case 2

(63+5)=4(17)

68=68

Again, it got verified, so the values are right.

______________________

♨ By forming quadratic equation

Given, the sum of two numbers is 80.

So, let one number be x, so the other number will be (80-x)

Let, x>(80-x)

Now, if 5 is added to the bigger number the smaller number will equal to it when, it will be miltiplied by 4, so

x+5=4(80-x)

x+5=320-4x -(3)

5x=315

So, x=63

So, the bigger number is 63, putting x=63 on the RHS of eq.(3)

x=17

Now, we don't need to verify this

So, again, the bigger and smaller number are 63 and 17 respectively.

Answer 2

Answer: 15

Given :-

The sum of two numbers is 80.

If the larger number exceeds four times the smaller number by 5.

To Find: Smaller Number

Solution :-

Let the larger number be x and the smaller number be y.  

According to the question,  

x + y = 80…(i)  

x = 4y + 5  

» x – 4y = 5...(ii)  

Subtracting (ii) from (i), we get  

» 5y = 75  

» y = 75/5

» y = 15

 

Putting y value in Eq (i)

» x + y = 80

» x + 15 = 80

» x = 80 - 15  

» x = 65  

Hence, the numbers are 65 and 15.

We're told to find smaller number.

Thus, Answer: 15