Question

the product of two positive numbers is 5 / 6 and their quotient is 15 / 8.Calculate the numbers with solution

Answer 1

Let "x" and y" be the two numbers.

We have

xy = 5%2F6, (1) and
x%2Fy = 15%2F8. (2)

Multiply (1) and (2) (both sdes). You will get

x%5E2 = %285%2A15%29%2F%286%2A8%29 = 25%2F16.

Hence, x = +/- 5%2F4.

Next, divide (1) by (2) (both sides). You will get

y%5E2 = 5%2F6 : 15%2F8 = %285%2A8%29%2F%286%2A15%29 = 4%2F9.

Hence, y = +/- 2%2F3.

Answer. There are two solutions: (x,y) = (5%2F4,2%2F3) and (x,y) = (-5%2F4,-2%2F3).

// We should exclude the second solution, since the numbers are negative.

Answer 2

Concept

Multiplication and Division are some of the basic arithmetic operations used in mathematics. Other operations are Subtraction and Addition.

Given

1) Product of two numbers is 5/6

2) Quotient of two numbers is 15/8

Find

Value of two numbers

Solution

Let the numbers be m and n

Product of m an n

P = mn

mn = 5/6 ..........(1)

Quotient of m and n

Q = m/n

m/n = 15/8 ..........(2)

Multiplying (1) and (2)

mn * m/n = 5/6 * 15/8

m² = (5*15) / (6*8)

m² = 75/48

m² = 25/16

m = 5/4

mn = 5/6

n = 5/6m

n = 5/(6 * 5/4)

n = 20/30

n = 2/3

The numbers are 5/4 and 2/3 whose product is 5/6 and quotient is 15/8.

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