4. Two consultants were hired by a company. The total consultant fees were $18,500. If one consultant had earned $500 less, each consultant would have been paid the same. How much was each consultant paid?
6. Five cars in a race all finished within 8 seconds of each other. Car 1 finished 1 second ahead of car 4, and car 4 was not last. Car 2 finished 6 seconds before car 5. Car 5 finished 3 seconds behind car 1. Car 1 finished 5 seconds behind car 3. In what order did the cars finish?
amount earned by 1st --- x
amount earned by 2nd --- 18500-x
if first had earned 500 less, they would be the same
x - 500 = 18500 - x
2x = 19000
x = 9500
one earned 9500 , the other 9000
6.
time for car 3 --- x
time for car 1 --- x+5
time for car 5 --- x +8
time for car 4 ---- x+1
time for car 2 ---- x+2
looks like the order was
3,4,2,1,5
4. Let's assume the amount of money paid to one consultant is x. According to the problem, the total consultant fees were $18,500. Therefore, we have the equation: x + (x-500) = 18,500.
To find the amount paid to each consultant, we need to solve this equation. We can simplify it by combining like terms: 2x - 500 = 18,500.
Next, we add 500 to both sides of the equation to isolate the variable: 2x = 18,500 + 500.
Simplifying further, we have: 2x = 19,000.
To solve for x, we divide both sides of the equation by 2: x = 19,000 / 2.
Calculating this, we find that x = 9,500.
So, one consultant was paid $9,500, and the other consultant was paid $500 less, which is $9,000.
6. To determine the order in which the cars finished, we need to examine the given information.
From the information provided, we know:
- Car 1 finished 1 second ahead of Car 4.
- Car 4 was not last.
- Car 2 finished 6 seconds before Car 5.
- Car 5 finished 3 seconds behind Car 1.
- Car 1 finished 5 seconds behind Car 3.
Let's organize these clues to form a logical sequence:
- Car 2 > Car 5. (Car 2 finished 6 seconds before Car 5).
- Car 5 > Car 1. (Car 5 finished 3 seconds behind Car 1).
- Car 1 > Car 4. (Car 1 finished 1 second ahead of Car 4).
- Car 1 > Car 3. (Car 1 finished 5 seconds behind Car 3).
From these clues, we have: Car 2 > Car 5 > Car 1 > Car 4 > Car 3.
Therefore, the order in which the cars finished the race is Car 2, Car 5, Car 1, Car 4, and Car 3.