Question

jamal distributes items collected by a charity. an expression modeling the number of items remaining is given, where w represents the number of weeks that jamal has distributed the items.
800 - 60w
what does the coefficient of the term -60w represent?
ⓐ the number of weeks it takes jamal to distribute 800 items
ⓑ the number of weeks it takes jamal to distribute 60 items
ⓒ the number of items jamal distributes every week
ⓓ the total number of items jamal distributes

Explanation:

Step1: Analyze the expression

The expression for remaining items is \( 800 - 60w \), where \( w \) is the number of weeks. The term \( -60w \) is formed by multiplying the number of weeks (\( w \)) by 60. So 60 here should represent the number of items distributed per week, and multiplying by \( w \) (weeks) gives the total number of items distributed in \( w \) weeks. But the question is about the coefficient's meaning in \( -60w \). Wait, no—wait, the coefficient of \( w \) in \( -60w \) is -60, but the term's meaning: let's check options. Option c says "the number of items Jamal distributes every week"—wait, no, 60 is the number per week, so \( 60w \) is total distributed in \( w \) weeks, but the term \( -60w \) is the subtraction of total distributed from 800. But the question is about what the coefficient (60) in \( -60w \) represents? Wait, no, the term is \( -60w \), so the coefficient of \( w \) is -60, but the number 60 here: let's see options. Option c: "the number of items Jamal distributes every week"—yes, because if he distributes 60 per week, then in \( w \) weeks, he distributes \( 60w \) items, so the term \( -60w \) is the total items distributed (so the coefficient 60 is the weekly distribution). Wait, but let's check other options. Option a: time to distribute 800 items—no, that would be \( 800/60 \), not 60. Option b: time to distribute 60 items—no, that would be 1 week if 60 per week. Option d: total distributed—no, total distributed is \( 60w \), not 60. So the coefficient 60 in \( -60w \) represents the number of items per week. So option c.

Step2: Confirm with options

• Option a: Time to distribute 800 items would be \( 800/60 \), not 60. Eliminate.
• Option b: Time to distribute 60 items—if he distributes 60 per week, time is 1 week, not 60. Eliminate.
• Option c: 60 is the number of items per week, so \( 60w \) is total in \( w \) weeks. The term \( -60w \) subtracts total distributed from 800. So 60 is weekly distribution. Correct.
• Option d: Total distributed is \( 60w \), not 60. Eliminate.

Answer:

c. the number of items Jamal distributes every week