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Darryl has written 60 percent, or 12 pages, of his history report. Darryl wants to figure out how many total pages he needs to write. Darryl’s work is shown below.

Step 1: Write 60 percent as a ratio. StartFraction part Over whole EndFraction = StartFraction 60 Over 100 EndFraction

Step 2: Write an equivalent ratio using the number of pages done so far. StartFraction 60 Over 100 EndFraction = StartFraction 12 Over question mark EndFraction

Step 3: Divide the part by 5 to get 12.

Step 4: Divide the whole by 12 to get the total number of pages.

What mistake did Darryl make?
In Step 1, Darryl should have written the ratio as StartFraction 100 Over 60 EndFraction.
In Step 2, Darryl should have put 12 in the denominator.
In Step 3, Darryl should have divided the part by 12.
In Step 4, Darryl should have divided the whole by 5.

1 answer

Darryl made a mistake in Step 4. Here's the reasoning:

  1. In Step 1, Darryl correctly wrote 60 percent as a ratio: \(\frac{60}{100}\).

  2. In Step 2, he set up the equivalent ratio correctly: \(\frac{60}{100} = \frac{12}{?}\). The question mark represents the total number of pages.

  3. In Step 3, he intended to find the total number of pages by relating the part to the whole, but instead of dividing the part (12) by 5, he should have recognized that since 60 is 12 pages, the total number of pages (the whole) should actually come from the relationship that 12 represents 60% of the total.

  4. In Step 4, Darryl incorrectly mentions dividing the whole by 12 to find the total number of pages, which is also incorrect. Instead, he should have recognized that if 12 pages is 60%, then to find 100% (the total), he should divide by 60 and then multiply it by 100.

To sum up:

  • The correct approach from Step 2 would involve setting up the equation \(60/100 = 12/x\) and solving for \(x\).
  • Thus, Darryl's mistake lies in the process he used to find the total number of pages in both Step 3 and Step 4.

So, the correct answer is: In Step 4, Darryl should have divided the whole (100) by 60 and then multiplied by 12 to get the total number of pages. None of the other statements accurately pinpoint the main error in his calculation method.