Math homework help??

Question

This exercise is intended to challenge your ability to interpret the meaning of functions in words.

In March 2006, the Bureau for Economic Analysis (BEA) issued a press release detailing per capita income rankings for the states. An excerpt from the report is provided here.
Connecticut led the nation with a per capita income . . . 38 percent above the national average. Louisiana's per capita income was . . . 28 percent below the national average . . .†
Write the equation of a function that relates the per capita income of Connecticut, C, to the per capita income of Louisiana, L.

Answer 1

Let's take N to be the national average of per capita income.

 

This gives us the following equations for C and L:

 

C = N + 0.38N = 1.38N

 

L = N - 0.28N = 0.72N

 

Now we have two equations with a shared variable, so we can substitute N in one of them and combine them to relate C to L:

 

Since L = 0.72N, or alternately, N = 1/0.72L, C = 1.38N = 1.38 * (1/0.72)L = 1.92L.

 

So our final equation relating the two is C = 1.92L, or alternately, L = 0.52C.

 

To check our work, we need simply plug in some sample values and make sure they check out.

 

Say N = 50 (50 thousand, 50 million, doesn't really matter). Just to keep things simple.

 

C = 1.38N = 1.38 (50) = 69

L = 0.72N = 0.72 (50) = 36

 

Now that we have values for C and L, we plug them into our final equation and verify that they come out equal:

 

C = 1.92L

(69) = 1.92 (36)

69 = 69

 

It comes out exact, but I rounded up: 1.92 is actually 1.91666(6...)7 repeating.