A group of friends are planning a road trip. If they all contributed $24, then they would be $6 short of the total. If they all contributed $25, then they would have $3 more than needed. What is the total cost of the trip?
C = Cost
n = nubers of friends
If they all contributed $24, then they would be $6 short of the total:
n * 24 = C - 6 Add 6 to both sides
24 n + 6 = C - 6 + 6
24 n + 6 = C
C = 24 n + 6
If they all contributed $25, then they would have $3 more than needed.
n * 25 = C + 3
25 n = C + 3 Subtract 3 to both sides
25 n - 3 = C + 3 - 3
25 n - 3 = C
C = 25 n - 3
C = C
24 n + 6 = 25 n + 3 Subtract 24 n to both sides
24 n + 6 - 24 n = 25 n - 3 - 24 n
6 = n - 3 Add 3 to both sides
6 + 3 = n - 3 + 3
9 = n
n = 9
Group have 9 friends
C = 24 n + 6
C = 24 * 9 + 6
C = 216 + 6
C = 222 $
OR
C = 25 n - 3
C = 25 * 9 - 3
C = 225 - 3
C = 222 $
The total cost of the trip is 222 $
Cool I got the right answer not using cheat . im ready to the next level
To find the total cost of the trip, we can set up a system of equations based on the given information.
Let's assume that there are 'n' friends planning the road trip and 'c' is the cost of the trip.
According to the first condition, if they all contributed $24, then they would be $6 short of the total. This can be expressed as:
24n = c - 6 (equation 1)
According to the second condition, if they all contributed $25, then they would have $3 more than needed. This can be expressed as:
25n = c + 3 (equation 2)
Now, let's solve the system of equations to determine the values of 'n' and 'c'.
To eliminate 'c' from the equations, we can subtract equation 1 from equation 2:
25n - 24n = c + 3 - (c - 6)
n = 9
Substituting the value of 'n' into equation 1, we can solve for 'c':
24(9) = c - 6
216 = c - 6
c = 222
Therefore, the total cost of the trip is $222.