Chapter 5.7, Problem 35E

To determine

To find: the money can spend on savings and housing.

Answer to Problem 35E

The amounts that can be spent on savings and housing are 300 dollars and 500 dollars.

Explanation of Solution

Given information:

The spending amount should be less than half of monthly $2000 payback on housing and savings. At least 10% paycheck on savings and at most 30% of it on housing should be done.

Calculation:

The amount spent on savings and housing is less than half of 2000 dollars.

The amount spent on savings is at least 10% of 2000 dollars.

The amount spent on housing is at most 30% of 2000 dollars.

Let $x$ be the amount spent on savings and $y$ be the amount spent on housing. Then the system of inequalities that model the given problem is

  $\begin{array}{l}x\ge 200\text{Since}x\text{must}\text{be}\text{at}\text{least}\text{10\%}\text{of}\text{2000}\\ y\le 200\text{Since}y\text{must}\text{be}\text{at}\text{least}\text{10\%}\text{of}\text{2000}\\ x+y<1000\text{Since}x+y\text{must}\text{be}\text{less}\text{than}\text{half}\text{of}\text{2000}\end{array}$

Graph the inequalities $x\ge 200,y\le 200\text{and}\text{}x+y<1000$ as shown in the below figure. The ordered pair $\left(x,y\right)=\left(300,500\right)$ dollars is a solution. It means 300 dollars can be spent on savings and 500 dollars can be spent on housing.

  

Therefore, the amounts that can be spent on savings and housing are 300 dollar and 500 dollar.