A bottle of the medicine contains 0.5 kilograms of the medicine. One dose of the medicine is 20 grams for a child and 45 grams for an adult. The number of grams used can be calculated with the formula 20C + 45A, where A is the number of adult doses and C is the number of child doses. If a medical assistant needs to give a dose of the medicine to 12 adults and 10 children, will there be enough medicine in the bottle? If not, how many more grams will be needed?

We have been given that a bottle of the medicine contains 0.5 kilograms of the medicine. One dose of the medicine is 20 grams for a child and 45 grams for an adult. The number of grams used can be calculated with the formula 20C + 45A, where A is the number of adult doses and C is the number of child doses.

First of all let us convert 0.5 kilograms to grams.

[tex]\text{0.5 kilograms}=(1000\times 0.5)\text{ grams}=500\text{ grams}[/tex]

To find if the medicine in bottle is enough for 12 adults and 10 children let us equate the total medicine in bottle with amount needed by assistant.

[tex]20\times 10+45\times 12=500[/tex]

[tex]200+540=500[/tex]

[tex]740\neq 500[/tex]

[tex]740> 500[/tex]

We can see that amount of medicine in the bottle is not enough for 12 adults and 10 children.

2. To find the amount of more medicine needed we will subtract the amount of medicine in bottle from the amount of medicine needed for 12 adults and 10 children.

[tex]\text{More medicine needed}=740-500=240[/tex]

Therefore, the medical assistant will need 240 grams of more medicine to accommodate 12 adults and 10 children.