SOLUTION: The Morris family spent 9 days at Lake Tahoe and San Francisco. They spent $350 per day at Lake Tahoe and $475 per day in San Francisco. The total cost of their trip was $3,650.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The Morris family spent 9 days at Lake Tahoe and San Francisco. They spent $350 per day at Lake Tahoe and $475 per day in San Francisco. The total cost of their trip was $3,650.       Log On


   

Question 1153741: The Morris family spent 9 days at Lake Tahoe and San Francisco. They spent $350 per day at Lake Tahoe and $475 per day in San Francisco. The total cost of their trip was $3,650.

a. Write a system of equations that can be used to find how many days the Morris family spent at Lake Tahoe and in San Francisco. Be sure to define the variables you use.

b. Use the substitution method to find the number days the Morris family spent at Lake Tahoe and in San Francisco. Be sure to show (write out) your work.
Answer by ikleyn(52792) About Me  (Show Source):
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Let x be the number of days in San Francisco and let y be the number of days at Lake Tahoe.


From the condition, you have this system od 2 equations in 2 unknowns


      x +    y =    9      (1)    (nimber of days, total)

   475x + 350y = 3650      (2)   (dollars spent, total)


To solve the system apply the Substitution method.

For it, express y = 9-x from equation (1), and substitute it into equation (2), replacing y. You will get


    475x + 350*(9-x) = 3650.


Simplify step by step and solve for x


    475x + 3150 - 350x = 3650

     125x              = 3650 - 3150 = 500

        x                            = 500%2F125 = 4.


ANSWER.  4 days in San Francisco, and the rest, (9-4) = 5 days at the Lake Tahoe.

Solved.