Solve the problem

Question

Suppose economics use a model of a country’s economy the equation C=0.6716D + 5.9845

When C represents the consumption of products int he billions of dollars and D represents disposable income in billions dollars. Solve the equation for D and use the result to determine the disposable income D if the consumption C is $8.42 billion. Round you answer to the nearest tenth of a billion.

Answer 1

Hi Ashley.

Don't let the big numbers scare you.

Suppose economics use a model of a country’s economy the equation C=0.6716D + 5.9845

When C represents the consumption of products int he billions of dollars and D represents disposable income in billions dollars. Solve the equation for D and use the result to determine the disposable income D if the consumption C is $8.42 billion. Round you answer to the nearest tenth of a billion.

Start with what you know. Given:

1. C = 0.6716*D + 5.9845
2. C is $8.42 billion ===> C = 8.42 (billion dollars)

Solve the equation for D:

1. C = 0.6716*D + 5.9845
2. D*0.6716 = C - 5.9845
3. D = (C - 5.9845) / 0.6716

Use the result (substitute 8.42 for C) to determine the disposable income D:

1. D = (C - 5.9845) / 0.6716
2. D = (8.42 - 5.9845) / 0.6716
3. D = 2.4355 / 0.6716
4. D = 3.62644145532459797

Round you answer to the nearest tenth of a billion.

1. D = 3.62644145532459797 = $3.6 billion

Check your work:

1. 8.42 = 0.6716*3.6 + 5.9845
2. 8.42 = 2.41776 + 5.9845
3. 8.42 ≅ 8.40226 because both round to the nearest tenth as 8.4✔

NOTE: Rounding before you have finished all of your calculations will always introduce an error into your calculations.

Answer 2

$8.42*10^9=.6716*10^9*D*10^9+5.9845*10^9

-5.9845

=2.4355 = .6716D

/.6716=3.626..............=D

I made 5.09845 into ^9. Was I supposed to?

Answer 3

Start by writing out your formula:

C = .6716D + 5.9845

Plug in C, which the problem tells you

8.42 = .6716D + 5.9845

subtract 5.9845 from both sides

2.4355 = .6716D

divide both sides by the number in front of D so you're left with 1D

2.4355 / .6716 = .6716D / .6716

answer

3.6264 = D

round to the nearest tenth

D = $3.6 billion