Question

The Morris family spent 9 days at Lake Tahoe and San Francisco. The total cost of the 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 of days the Morris family spent at Lake Tahoe and in San Francisco. Be sure to show your work. ​

Answer 1

Answer:

a) A + B = 9

350A + 475B = 3650

where A = number of days spend at Lake Tahoe

B = number of days spent in San Francisco

b) A = 5 days

B = 4 days.

Hence, the Morris family spent 5 days at Lake Tahoe and spent 4 days at San Francisco

Step-by-step explanation:

a) Let the number of days spend at Lake Tahoe be A

And the number of days spend at San Francisco be B

Total number of days spend on the trip = 9

A + B = 9

Total cost of the whole 9-day trip = $3650

Cost per day at Lake Tahoe = $350

Total cost of staying A days at Lake Tahoe = $350A

Cost per day of staying at San Francisco = $475

Total cost of staying B days in San Francisco = $475B

350A + 475B = 3650

The two equations are

A + B = 9

350A + 475B = 3650

b) Use the substitution method to solve this.

A + B = 9 (eqn 1)

350A + 475B = 3650 (eqn 2)

Make A the subject of formula in eqn 1

A = 9 - B

Then, substitute this for A in eqn 2

350A + 475B = 3650

350(9 - B) + 475B = 3650

3150 - 350B + 475B = 3650

125B = 500

B = (500/125) = 4

A = 9 - B = 9 - 4 = 5

Hence, they spent 5 days at Lake Tahoe and spent 4 days at San Francisco.

Hope this Helps!!!

Answer 2

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.

Step-by-step 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

$P = \frac{500}{125}$

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.