Question:
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 your work.
Answer:
a) P + Q = 9
475P + 350Q = 3650
b) 4 days in San Francisco and 5 days in Tahoe.
Explanation:
We know the 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
Let's take P as the number of days spent in San Francisco.
Let's take Q as the number of days spent in Tahoe.
Since the total number of days spent is 9 days, hence, P+Q=9 ................(1)
Since they spent $475 per day in San Francisco and $350 per day in Tahoe, and we are told the total amount spent is $3650.
Therefore, total amount will be:
475P + 350Q = 3650...........(2)
We now have:
P + Q = 9 ..............................(1)
475P + 350Q = 3650...........(2)
Using substitution method to solve the equation.
P + Q = 9
Q = 9 -P
Let's substitute (9-P) for Q in equation (2).
Therefore, we now have:
475P + 350×(9-P) = 3650
= 475P + 3150 - 350P = 3650
475P - 350P = 3650 - 3150
= 125P = 500
P = 4
Substituting 4 for P in equation (1), we have:
4 + Q = 9
= Q = 9 -4
Q= 5.
P=4 and Q=5
Therefore, they spent 4 days in San Francisco and 5days in Tahoe.