Question

the pharmacist says 5 g of a powder with 45cm³ of water to make a prescription medicine. How much powder mix with 81cm² of water to make a larger amounts of the same medicine?​

Answer 1

For 81cm³ of water we need 9g of powder.

Explanation:

To have the same medicine in a larger amount, the concentration of the powder must be the same, and this concentration is given by the ratio between the amount of powder and the volume of water it is diluted. This ratio is

`(5)/(45) = (1)/(9)`

Since this ratio must be the same for a larger amount, the ratio of our desired amount of powder(let's call it x) by 81cm³ must be equal to this ratio.

`(x)/(81) = (1)/(9)`

Solving for x, we have

`(x)/(81) = (1)/(9) \\\\`

`(x)/(81)` ×
`81= (1)/(9)` ×
`81`

`x = (81)/(9)`

`x = 9`

For 81cm³ of water we need 9g of powder.