Question

of three positive numbers, the product of the first and second is 8/15, the product of first and third is 1/3 and the product of second and third is 2/5. Find the numbers


Please help me...I have my UT tomorrow

Answer 1

ANSWER:

x = 2/3

y = 4/5,

z = 1/2

ASSUMPTION:

Let the numbers be x, y, z

GIVEN:

xy = 8/15

yz = 2/5

xz = 1/3

TO FIND:

The values of x,  y, z

EXPLANATION:

x = 8/15y

x = 1 /3z

Equate both the x values

8/15y = 1/3z

8z/5  = y

Substitute 8z/5  = y in yz = 2/5

(8z/5)z = 2/5

8z² = 2

z² = 1/4

z = 1/2

Because the given numbers are positive

substitute z = 1/2 in yz = 2/5

y/2 = 2/5

y = 4/5

Substitute z = 1/2 in xz = 1/3

x/2 = 1/3

x = 2/3

HENCE   x = 2/3, y = 4/5, z = 1/2

VERIFICATION:

Substitute x = 2/3, y = 4/5 in xy = 8/15

2/3 × 4/5 = 8/15

8/15 = 8/15

HENCE VERIFIED.