Question

Try the numbers 22, 23, 24, 25 in the equation 4/3 = 32/d to test whether any of them is a solution. a. 23 is a solution. c. 24 is a solution. b. 25 is a solution. d. 22 is a solution.

Answer 1

c. 24 is a solution

Explanation:

Given equation:

`(4)/(3)=(32)/(d)`

To test the numbers 22, 23, 24, 25 for the solution.

Solution:

In order to test the given number for the solution, we will plugin each number in the unknown variable
`d` and see if it satisfies the equation.

1)
`d=22`

`(4)/(3)=(32)/(22)`

Reducing fraction to simplest form by dividing the numerator and denominator by their G.C.F.

`(4)/(3)=(32/ 2)/(22/ 2)`

`(4)/(3)=(16)/(11)`

The above statement can never be true and hence 22 is not a solution.

2)
`d=23`

`(4)/(3)=(32)/(23)`

The fractions can no further be reduced.

The statement can never be true and hence 23 is not a solution.

3)
`d=24`

`(4)/(3)=(32)/(24)`

Reducing fraction to simplest form by dividing the numerator and denominator by their G.C.F.

`(4)/(3)=(32/ 8)/(24/ 8)`

`(4)/(3)=(4)/(3)`

The above statement is always true and hence 24 is a solution.

4)
`d=25`

`(4)/(3)=(32)/(25)`

The fractions can no further be reduced.

The statement can never be true and hence 25 is not a solution.