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If p pencils cost c cents at the same rate, how many pencils can be bought for d dollars?

A) \(cdp\)

B) \(100 cdp\)

C) \(\frac{dp}{100c}\)

D) \(\frac{100cd}{p}\)

E) \(\frac{100 dp}{c}\)

These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach.

Let's use the INPUT-OUTPUT approach.

Pick some numbers that meet the given information. Say p = 3 and c = 50 This means that we can buy 3 pencils for 50 cents ($0.50)

Let's also say that d = 1 This means that the question is now asking "How many pencils can be bought for 1 dollar" If we can buy 3 pencils for 50 cents, then we can buy 6 pencils for 1 dollar

So, when p = 3, c = 50 and d = 1, the answer to our question is 6 pencils.

Now let's take each answer choice and see which one yields an OUTPUT of 6, when we input p = 3, c = 50 and d = 1

A) cdp = (50)(1)(3) = 150. We need an output of 6. ELIMINATE.

B) 100cdp = (100)(50)(1)(3) = 15000. We need an output of 6. ELIMINATE.

C) dp/100c = (1)(3)/(100)(50) = 3/5000. We need an output of 6. ELIMINATE.

D) 100cd/p = (100)(50)(1)/(3) = 5000/3. We need an output of 6. ELIMINATE.