A minivan left a condominium with a number of passengers. 7 passengers got off and 10 passengers boarded the minivan at Evergreen Road. At Woodville Interchange, 1/4 of the number of passengers got off and 12 passengers were left in the minivan. How many passengers were on the minivan when it left the condominium?
just do the adding and subtracting! Starting with x passengers,
x - 7 + 10 = x+3
(x+3) * 3/4 = 12
x = 13
13
Let's solve this problem step by step.
Step 1: Start with the number of passengers when the minivan left the condominium.
Let's represent the number of passengers when the minivan left the condominium as "x".
Step 2: Subtract the number of passengers who got off at Evergreen Road.
Since 7 passengers got off at Evergreen Road, we subtract 7 from x.
The new number of passengers is now x - 7.
Step 3: Add the number of passengers who boarded at Evergreen Road.
Since 10 passengers boarded at Evergreen Road, we add 10 to the previous total.
The new number of passengers is now (x - 7) + 10.
Step 4: Subtract 1/4 of the number of passengers at Woodville Interchange.
We multiply the previous total by 1/4 and subtract it from the previous total.
The new number of passengers is now [(x - 7) + 10] - (1/4)[(x - 7) + 10].
Step 5: Set the remaining passengers at Woodville Interchange to be 12.
We equate the new number of passengers to 12 and solve for x.
[(x - 7) + 10] - (1/4)[(x - 7) + 10] = 12.
Step 6: Solve the equation.
Simplifying the equation, we have:
[(x - 7) + 10] - (1/4)[(x - 7) + 10] = 12.
(x - 7) + 10 - (1/4)(x - 7) - (1/4)(10) = 12.
(x - 7) + 10 - (1/4)(x - 7) - 2.5 = 12.
x - 7 + 10 - (1/4)x + (7/4) - 2.5 = 12.
x - (1/4)x + 10 + (7/4) - 9.5 = 12.
(3/4)x + (1/4) = 12.
(3/4)x + (1/4) - (1/4) = 12 - (1/4).
(3/4)x = 47/4.
Multiplying both sides of the equation by 4/3, we have:
x = 47/4 * 4/3.
x = 47/3.
Therefore, the minivan had 47/3 (or approximately 15.67) passengers when it left the condominium.
To determine the number of passengers on the minivan when it left the condominium, we'll work backwards from the information given.
Let's set up an equation to represent the problem. Let's assume the number of passengers on the minivan when it left the condominium is represented by "x."
According to the given information:
After 7 passengers got off, the minivan had (x - 7) passengers remaining.
After 10 passengers boarded at Evergreen Road, the minivan had (x - 7 + 10) passengers.
At Woodville Interchange, 1/4 of the passengers got off, leaving 3/4 of the passengers remaining. Therefore, the number of passengers remaining is (3/4)(x - 7 + 10).
We are also given that 12 passengers were left in the minivan after the Woodville Interchange, so we can set up the equation:
(3/4)(x - 7 + 10) = 12
To solve for x, we can start by simplifying the equation:
(3/4)(x + 3) = 12
Multiply both sides by 4/3 to get rid of the fraction:
x + 3 = (4/3)(12)
x + 3 = 16
Finally, subtract 3 from both sides:
x = 16 - 3
x = 13
Therefore, there were 13 passengers on the minivan when it left the condominium.