I need help with math question??? See Below....?

Question

A new medication X Disodium, comes as a powder which must be reconstituted as follows: For Intravenous use:
Ad 24mL of sterile water for injection, USP. Each 2.5mL of resulting solution contains 500mg of X. Prior to administration dilute further to desired volume with an appropriate IV solution. How many mL must be injected into a 100mL IV bag of NS to equal 1.5g of X? ___mL

Answer 1

You need 7.5 ml of your solution to have 1.5 g (1500 mg) of X per 100 ml of NS.

SD/SH
>>SD = 1.5 g/ ? ml
>>SH = 500 mg/2.5 ml
>> Let x be the unknown volume

Convert the 1.5 g into mg first (1500 mg)To represent the formula:
1,500 mg / (x) ÷ 500 mg / 2.5 ml

It is a ratio and proportion so we will proceed with the operation by transposition of factors or (cross multiplication):
1,500 mg / (x) = 2.5 ml / 500 mg

Cancel the mg then proceed with multiplication:
{1,500 X 2.5 ml} = {(x) X 500}

That will give:
3,750 ml = 500x

Find the value of x by eliminating the 500 so divide both by 500:
3,750 ml / 500 =500x / 500

Cancel 500's on the right to leave the x- that will make:
3,750 ml / 500 = x

Proceed with division and the x value is:
x = 7.5 ml

Therefore you need:
7.5 ml of the X.