EXPLANATION:
Given;
We are told that a scientist needs 6000 calories per day.
We are also given a table showing the percentage of daily calories he can get from three types of food.
These are;
[tex]\begin{gathered} Biscuits---40\% \\ pemmican---45\% \\ Butter\text{ }and\text{ }cocoa---15\% \end{gathered}[/tex]Required;
We are required to calculate how many of each type of food he would need to eat each day.
Step-by-step solution;
We shall solve this by first determining how many calories can be gotten from each type of food based on the percentage given. This is calculated below;
[tex]\begin{gathered} Biscuits: \\ 6000\times\frac{40}{100}=2400 \end{gathered}[/tex]This means if he gets 75 calories from one biscuit, then to get 2,400 calories he would have to eat;
[tex]\begin{gathered} 75cal=1b \\ 2400cal=\frac{2400}{75} \\ 2400cal=32 \end{gathered}[/tex]The scientist would have to eat 32 biscuits to get 2400 calories.
[tex]\begin{gathered} Pemmican: \\ 6000\times\frac{45}{100}=2700 \end{gathered}[/tex]This means if he gets 135 calories from one pack of dried meat, then to get 2700 calories he would have to consume;
[tex]\begin{gathered} 135cal=1pack \\ 2700cal=\frac{2700}{135} \\ 2700cal=20 \end{gathered}[/tex]Therefore, the scientist would have to eat 20 packs of pemmican to get 2700 calories
[tex]\begin{gathered} Butter\text{ }and\text{ }Cocoa: \\ 6000\times\frac{15}{100}=900 \end{gathered}[/tex]This means if he eats 1 package of Butter and cocoa he gets 225 calories. To get 900 calories he would have to eat;
[tex]\begin{gathered} 225cal=1pack \\ 900cal=\frac{900}{225} \\ 900cal=4 \end{gathered}[/tex]Therefore, the scientist would have to eat 4 packs of Butter and cocoa.
We now have the summary as follows;
ANSWER:
[tex]\begin{gathered} Biscuits=32 \\ Pemmican=20\text{ }packs \\ Butter\text{ }and\text{ }cocoa=4\text{ }packs \end{gathered}[/tex]