Question

The future of Social Security and Medicare generates a lot of debate and political posturing. Analysts predict that, without significant change, Social Security and Medicare funds will be exhausted at some future date (the date depends on the expert). The exercise asks you to use linear trends based on Social Security Administration historical data in order to estimate when, if ever, the funds will be in trouble (i.e., when disbursements will exceed income). Social Security income for the years 1990-2000 suggest that the income trend can be estimated by the equation y = 21.29x + 264.6 where x is the number of years since 1990 and y = annual income in billions of dollars. For the same years, the Social Security disbursements have the linear trend y = 13.25x + 226.54. (a) Find the point where income = disbursements. (Enter your answer as an ordered pair. Round your answers to two decimal places.) (x, y) =

Answer 1

To find the point where income equals disbursements, set the income equation equal to the disbursements equation and solve for x.

Step-by-step explanation:

The question asks us to find the point where income equals disbursements. To do this, we need to set the income equation equal to the disbursements equation and solve for x.

So, we have:

21.29x + 264.6 = 13.25x + 226.54

Subtracting 13.25x from both sides, we get:

8.04x + 264.6 = 226.54

Subtracting 264.6 from both sides, we get:

8.04x = -38.06

Dividing both sides by 8.04, we get:

x = -4.74

Therefore, the point where income equals disbursements is approximately (-4.74, -38.06).