Math Problem Statement

Use the following graph to estimate the publicly held debt​ (in dollars) in 1980 and 2015. About how much larger was the 2015 held debt than the 1980 publicly held debt in actual​ dollars? Express this difference as a percentage of the 1980 GDP. Assume that the GDP in​ 1945, 1980, and 2015 was​ $226 billion,​ $2791 billion, and​ $18,100 billion, respectively. The publicly held debt was about ▼ $1396 $558 $698 $279 billion in 1980 and about ▼ $18,100 $9050 $27,150 $14,118 billion in 2015.​ So, the publicly held debt in 2015 was about ​$    enter your response here more than in​ 1980, which is    enter your response here​% of the 1980 GDP. ​(Round to the nearest whole numbers as​ needed.)

Solution

We are tasked with estimating the publicly held debt in 1980 and 2015, calculating how much larger the 2015 debt is compared to 1980, and expressing that difference as a percentage of the 1980 GDP.

Step 1: Find the debt in 1980 and 2015

According to the problem, the publicly held debt was:

  • $698 billion in 1980.
  • $18,100 billion in 2015.

Step 2: Calculate the difference in debt between 2015 and 1980

We subtract the 1980 debt from the 2015 debt to find how much larger the 2015 debt is: Difference=18,100698=17,402 billion dollars\text{Difference} = 18,100 - 698 = 17,402 \text{ billion dollars}

Thus, the 2015 publicly held debt was $17,402 billion more than the 1980 debt.

Step 3: Express the difference as a percentage of the 1980 GDP

We are given that the GDP in 1980 was $2,791 billion. To express the difference in debt as a percentage of the 1980 GDP, we use the formula: Percentage difference=(17,4022,791)×100\text{Percentage difference} = \left( \frac{17,402}{2,791} \right) \times 100 Percentage difference=623.5%\text{Percentage difference} = 623.5\%

Thus, the difference in debt between 2015 and 1980 is approximately 624% of the 1980 GDP.

Final Answer:

  • The publicly held debt in 2015 was about $17,402 billion more than in 1980.
  • This difference is about 624% of the 1980 GDP.

Would you like further details on any step or additional clarification?

Here are 5 related questions to expand on the topic:

  1. How does the change in publicly held debt compare to the change in GDP between 1980 and 2015?
  2. What factors could contribute to such a significant increase in publicly held debt over time?
  3. How does the U.S. debt-to-GDP ratio in 2015 compare to that in 1980?
  4. What is the significance of the publicly held debt as a percentage of GDP?
  5. How does the increase in publicly held debt affect the economy and government spending?

Tip: When calculating large differences like this, it's crucial to keep track of units (billions, trillions) and check for any percentage increase relative to a baseline year to fully understand the economic impact.

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Math Problem Analysis

Mathematical Concepts

Percentage calculation
Debt-to-GDP ratio
Basic arithmetic

Formulas

Difference = Debt_2015 - Debt_1980
Percentage difference = (Difference / GDP_1980) * 100

Theorems

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Suitable Grade Level

Grades 9-12