Question

In 1982, if the 1.8 billion dollars collected as child support payments was only 10 percent of the total court-ordered payments due, approximately how many billion dollars of court-ordered payments for child support were not collected?

• A. 1.6
• B. 14.4
• C. 16.2
• D. 17.2
• E. 18.0

Hint:

For part-to-part percentage problems, using ratios is often the fastest method. If 10% is collected, 90% is not. The ratio of not collected to collected is 90:10 or 9:1. So, the uncollected amount is 9 times the collected amount.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a percentage problem. We are given the value of a part (the amount collected) and the percentage that part represents of the whole (the total amount due). We are asked to find the value of the remaining part (the amount not collected).
Step 2: Key Formula or Approach:
There are two common methods: 1. Find the total first. Let \(T\) be the total due. We are given \(0.10 \times T = 1.8\). Solve for \(T\), then calculate \(T - 1.8\). 2. Work with percentages directly. If 10% was collected, then \(100% - 10% = 90%\) was not collected. We can find the value of this 90%.
Step 3: Detailed Explanation:
We will use the second, more direct method. - Percentage of payments collected = 10%. - Value of payments collected = $1.8 billion. - Percentage of payments not collected = 100% - 10% = 90%. We can set up a proportion: If 10% corresponds to $1.8 billion, then 90% corresponds to an unknown amount, let's call it \(U\). Since 90% is exactly 9 times 10%, the value of \(U\) will be 9 times the value corresponding to 10%. \[ U = 9 \times ($1.8 \text{ billion}) \] \[ U = $16.2 \text{ billion} \] Step 4: Final Answer:
The total amount of court-ordered payments that were not collected is $16.2 billion.