Question

1. felix buys 5 boxes of pencils and 3 boxes of pens each month. each box of pencils contains p pencils, and each box of pens contains q pens. which two expressions represent the total number of writing utensils felix buys in 4 months?

a ( 4(5p + 3q) )
b ( 4(5) + 4(3q) )
c ( 20p + 12q )
d ( 9(p + q) )

Explanation:

Step1: Calculate monthly pencils and pens

Each month, Felix buys 5 boxes of pencils (p pencils per box) and 3 boxes of pens (q pens per box). So monthly pencils: \(5p\), monthly pens: \(3q\). Total monthly: \(5p + 3q\).

Step2: Calculate for 4 months

Multiply monthly total by 4: \(4(5p + 3q)\). Simplify: \(4\times5p + 4\times3q = 20p + 12q\), or factor as \(4(5p + 3q)\) (option A) or \(20p + 12q\) (option C). Wait, re - evaluate: Wait, the problem says "each box of pencils contains p pencils, each box of pens contains q pens". So monthly pencils: 5 boxes p = 5p, monthly pens: 3 boxes q = 3q. Total monthly writing utensils: \(5p+3q\). For 4 months: \(4\times(5p + 3q)=20p + 12q\), which is also equal to \(4(5p + 3q)\) (option A) and \(20p+12q\) (option C). Wait, let's check the options again. Option A: \(4(5p + 3q)\), Option C: \(20p + 12q\). Let's expand option A: \(4\times5p+4\times3q = 20p + 12q\), which matches option C. Wait, maybe a typo in the problem? Wait, the original problem's options: Let's re - read the image. The options are A. \(4(5p + 3q)\), B. \(4(5)+4(q)\), C. \(20p + 12q\), D. \(9(p + q)\). So first, monthly total: \(5p+3q\). For 4 months: \(4\times(5p + 3q)=20p + 12q\) (which is option C) and also \(4(5p + 3q)\) (option A). But let's check the calculation again. Monthly: 5 boxes of pencils (p each) → 5p, 3 boxes of pens (q each) → 3q. Total monthly: \(5p + 3q\). 4 months: \(4(5p + 3q)=20p+12q\). So both A and C are correct? Wait, maybe the problem has a typo, but let's see the options. Option A: \(4(5p + 3q)\), when expanded is \(20p + 12q\) (option C). So both are equivalent. But let's check the options given. If we have to choose, let's see the calculation steps.

First, find the number of writing utensils per month: number of pencils is \(5\times p = 5p\), number of pens is \(3\times q=3q\). So total per month: \(5p + 3q\). For 4 months, we multiply by 4: \(4\times(5p + 3q)=20p + 12q\), which is option C, and also \(4(5p + 3q)\) (option A) is the factored form.

Answer:

If we consider the factored form, the answer is A. \(4(5p + 3q)\) (or C. \(20p + 12q\) as they are equivalent). But based on the options, the correct expressions are A. \(4(5p + 3q)\) and C. \(20p + 12q\). If we have to choose one, let's go with A. \(4(5p + 3q)\) (or C. \(20p + 12q\))