Question

The letters R, M, O represent whole numbers .If R×M×O =240, R×O+M=46 and R+M×O=64 find R, M, O

Answer 1

Let, R = x ; M = y ; O = z
xyz = 240.......(1)
xz + y = 46.......(2)
x + yz = 64......(3)

From (1) :-
yz = 240/x......(4)
Now, put the value of yz in (3) from (4)

x + 240/x = 64
(x² + 240)/x = 64
x² + 240 = 64x
x² - 64x + 240 = 0
Value of x = 8.......(5)

Now, keep the value of (5) obtained in (4)
yz = 240/x
yz = 240/8
yz = 30
y = 30/z.......(6)

Put the value of (6) in (2)
xz + y = 46
8z + 30/z = 46
(8z² + 30)/z = 46
8z² + 30 = 46z
8z² - 46z + 30 = 0.......(7)
Divide the equation (7) with 2
4z² - 23z + 15 = 0
z = 10
So, R = 8 ; O = 10 and M = 3

Hope it helps !
#Shati
#Brainly benefactor

Answer 2

Let, R = x ; M = y ; O = z

xyz = 240.......(1)

xz + y = 46.......(2)

x + yz = 64......(3)

From (1) :-

yz = 240/x......(4)

Now, put the value of yz in (3) from (4)

x + 240/x = 64

(x² + 240)/x = 64

x² + 240 = 64x

x² - 64x + 240 = 0

Value of x = 8.......(5)

Now, keep the value of (5) obtained in (4)

yz = 240/x

yz = 240/8

yz = 30

y = 30/z.......(6)

Put the value of (6) in (2)

xz + y = 46

8z + 30/z = 46

(8z² + 30)/z = 46

8z² + 30 = 46z

8z² - 46z + 30 = 0.......(7)

Divide the equation (7) with 2

4z² - 23z + 15 = 0

z = 10

So, R = 8 ; O = 10 and M = 3

Hope it helps !