Exercise 9 Page 473

We are given that the trip from Des Moines to Phoenix, continuing on to Atlanta, and back to Des Moines was 3482 miles. Let's draw a diagram representing each leg of the trip. Draw a line between each city and label the equations which represent the corresponding distance.

As can be seen, a triangle has been made. It is a given that the sum of the legs lengths, which is the total trip distance, of the given triangle needs to be equal to 3482. ( 110x+53)+ 73.8x+( 150x+91)= 3482 We can now solve for the value of x by solving the previous equation. Remember to add and subtract like terms.

110x+53+73.8x+150x+91=3482

AddTerms

Add terms

333.8x+144=3482

SubEqn

LHS-144=RHS-144

333.8x=3338

DivEqn

.LHS /333.8.=.RHS /333.8.

x=10

We have found that the value of x is equal to 10. With this finding, we can then find the distance for each leg of a trip. We can do so by substituting 10 for x in each leg length of the triangle. Refer back to the first diagram for the equations.

Leg of the trip	x=10	Distance in miles
Des Moines - Phoenix	110( 10)+53	1153
Phoenix - Atlanta	150( 10)+91	1591
Atlanta - Des Moines	73.8( 10)	738