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Answer:
16 more items does Homeroom B need to collect to have more items per student
Step-by-step explanation:
Homeroom A Homeroom B
Students 24 16
Canned Food 30 22
Dry Food 42 24
Homeroom A collected 21 more items
So, total food Homeroom A has 30+42+21=93
Food item per student = [tex]\frac{93}{24}[/tex]
Let x be the extra food items need to be collected by homeroom B to have greater item per student than homeroom A.
Total food item of Homeroom B = 22+24+x
Food per student =[tex]\frac{22+24+x}{16}[/tex]
Since after having extra x food item the food item per student of Homeroom B will be greater than Homeroom A
⇒[tex]\frac{22+24+x}{16}>\frac{93}{24}[/tex]
⇒[tex]\frac{22+24+x}{16}>3.875[/tex]
⇒[tex]22+24+x>3.875*16[/tex]
⇒[tex]22+24+x>62[/tex]
⇒[tex]46+x>62[/tex]
⇒[tex]46+x>62[/tex]
⇒[tex]x>62-46[/tex]
⇒[tex]x>16[/tex]
Thus, 16 more items does Homeroom B need to collect to have more items per student
