The number of coronary-bypass operations performed in the United States increased from 13,000 in 1970 to 191,000 in 1983. What...

1. Translate the problem requirements: We need to find the percent increase from 13,000 operations in 1970 to 191,000 operations in 1983. Percent increase means: how much did the number grow as a percentage of the original amount?
2. Calculate the absolute increase: Find the difference between the final and initial values to determine how many more operations were performed.
3. Apply percent increase concept: Divide the absolute increase by the original amount and convert to percentage to find what percent the growth represents.
4. Match with answer choices: Compare our calculated percentage with the given options, using approximation since the question asks for an approximate answer.

Execution of Strategic Approach

1. Translate the problem requirements

Let's understand what we're looking for in everyday terms. We started with 13,000 coronary-bypass operations in 1970, and by 1983 we had 191,000 operations. The question is asking: by what percentage did this number grow?

Think of it this way - if you had $13 in your wallet in 1970, and by 1983 you had $191, you'd want to know what percent increase that represents. Percent increase tells us how much something grew compared to where it started.

Process Skill: TRANSLATE - Converting the real-world scenario into a mathematical percent increase problem

2. Calculate the absolute increase

First, let's find out exactly how many more operations were performed in 1983 compared to 1970. This is simply the difference between the two numbers:

Absolute increase = Final amount - Starting amount
Absolute increase = \(191,000 - 13,000 = 178,000\)

So there were 178,000 more operations performed in 1983 than in 1970. This is the raw increase in numbers, but we need to express this as a percentage of the original amount.

3. Apply percent increase concept

Now we need to figure out what this increase of 178,000 represents as a percentage of our starting point of 13,000.

Think about it this way: if our starting amount (13,000) represents 100%, then how many times bigger is our increase (178,000)?

Let's divide: \(178,000 ÷ 13,000\)

To make this easier, let's work with simpler numbers:
\(178 ÷ 13 ≈ 13.7\)

This means our increase is about 13.7 times as big as our original amount.
Since our original amount represents 100%, our increase represents about \(13.7 × 100\% = 1,370\%\)

So the percent increase is approximately 1,370%.

4. Match with answer choices

Looking at our calculated percent increase of approximately 1,370%, let's check which answer choice is closest:

(A) 90% - too small
(B) 140% - too small
(C) 150% - too small
(D) 1,400% - very close to our 1,370%
(E) 1,600% - too large

Since the question asks for an approximate percent increase, and our calculation gave us about 1,370%, choice (D) 1,400% is the closest match.

Final Answer

The approximate percent increase in coronary-bypass operations from 1970 to 1983 was 1,400%, which corresponds to answer choice (D).

This makes intuitive sense - the number of operations increased from about 13,000 to about 191,000, which means it increased by roughly 15 times the original amount, so a percent increase of about 1,400% is reasonable.

Common Faltering Points

Errors while devising the approach

Faltering Point 1: Confusing percent increase with percent of original
Students often misunderstand what "percent increase" means. They might think they need to find what percent 191,000 is of 13,000, rather than understanding that percent increase compares the change to the original amount. This leads them to calculate \(191,000 ÷ 13,000\) and think the answer is around 1,470%, missing that this represents the final amount as a percent of the original, not the increase.

Faltering Point 2: Forgetting the percent increase formula
Many students struggle to recall or correctly apply the percent increase formula: \(\frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} × 100\%\). Instead, they might try shortcuts or use incorrect formulas, such as simply finding the ratio of new to old values without subtracting the original amount first.

Errors while executing the approach

Faltering Point 1: Arithmetic errors with large numbers
When calculating \(191,000 - 13,000 = 178,000\), students may make simple subtraction errors with these large numbers. More critically, when dividing 178,000 by 13,000, students might struggle with the division or make errors when converting to simpler numbers \(178 ÷ 13\), potentially getting a significantly different result than 13.7.

Faltering Point 2: Incorrect handling of the division step
Students often get confused when they calculate \(178 ÷ 13 ≈ 13.7\) and need to convert this to a percentage. They might forget to multiply by 100% or incorrectly think that 13.7 directly represents 137% rather than 1,370%. This decimal-to-percentage conversion is a common source of errors.

Errors while selecting the answer

Faltering Point 1: Choosing answers that seem "more reasonable"
When students see their calculated answer of approximately 1,370%, they might doubt themselves because the percentage seems extremely large. This self-doubt could lead them to select one of the smaller options like (B) 140% or (C) 150%, thinking that a 1,400% increase "seems too big to be realistic" without recognizing that going from 13,000 to 191,000 truly represents such a dramatic increase.