Question

In​ 2012, a health insurance plan for a​ 35-year-old and his or her spouse costs ​$301 per month. That rate increased to ​$430 per month if a child were included and ​$538 per month if two children were included. The rate dropped to ​$269 per month for just the applicant and one child. Find the separate costs for insuring the​ applicant, the​ spouse, the first​ child, and the second child.

Answer 1

Answer: See explanation

Explanation:

Let the cost for insuring the applicant = a.

Let the cost for insuring the spouse = b

Let the cost for insuring the first child= c

Let the cost for insuring the second child = d

A 35-year-old health insurance plan and that of his or her spouse costs ​$301 per month. This means that:

a + b = $301.

That rate increased to ​$430 per month if a child were included. This means the cost of a child will be:

= $430 - $301

= $129

The rate increased to $538 per month if two children were included. This means the cost for the second child will be:

= $538 - $430

= $108

The rate dropped to ​$269 per month for just the applicant and one child. His will be the cost of the applicant and a single child. This can be written as:

a + $129 = $269

a = $269 - $129

a = $140

Since a + b = $301

$140 + b = $301

b = $301 - $140

b = $161

Applicant = $140

The spouse = $161

The first​ child = $129

The second child = $108