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 (write out) your work.

Answer 1

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 the Morris family spent "x" days at Lake Tahoe

And "y" days at San Francisco.

A total of 9 days were spent.

∴ x + y = 9 ..............a

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

∴ 350x + 475y = 3650 ..............b

using (a) in (b), we have,     (substitution method)

y = 9 - x

350 x + 475 (9 - x) = 3650

350x + 4275 - 475x = 3650

4275 - 3650 = 475x - 350x

625 = 125x

x = 625/125

x = 5

y = 9 - x = 9 - 5

y = 4

Therefore, 5 days were spent at Lake Tahoe and

4 days were spent at San Francisco.