Question

if x is a prime, y is a composite number such that x+y=240 and their LCM is 4199. Find and y

Answer 1

Factorise 4199= 13x17x19 =221x19

x=19
y=221

x+y=240

Answer 2

Answer:

The value of x=221 and y=19.

Step-by-step explanation:

Given : If x is a prime, y is a composite number such that $x+y=240$ and their LCM is 4199.

To Find : The value of x and y ?

Solution :

If x is prime number.

The factors is 1,x

If y is a composite number.

The factors are 1,a,b,c....,n

The HCF of x and y is 1.

The LCM of numbers is 4199.

We know, $\text{Product of numbers}=HCF\times LCM$

i.e. $x\times y=1\times 4199$

$xy=4199$ ......(1)

We have given, $x+y=240$ ......(2)

Solving (1) and (2),

$\frac{4199}{y}+y=240$

$4199+y^2=240y$

$y^2-240y+4199=0$

$y^2-240y+4199=0$

The point satisfying equation is (0,19)

i.e. y=19

Substitute in (2),

$x+19=240$

$x=240-19$

$x=221$

Therefore, The value of x=221 and y=19.