Question 29611: 7. Passengers boarded a plane in Phoenix. In Dallas, ½ of the passengers got off and 4/5 of the original number got on. In Memphis, ¾ of the passengers got off and twice the number of remaining passengers got on. In Chicago, ⅔ of the passengers got off the plane, leaving 39 passengers. How many passengers originally boarded the plane in Phoenix?
8. A group of students is trying to evenly divide the cookies remaining from a bake sale. If each student takes three cookies, there are five cookies left. If each student takes four cookies, they are two cookies short. How many students and how many cookies are there?
9. A used car salesman buys a car for $2500 and sells it for $4327. He then buys a camper with two-thirds of his profit and sells the camper for twice what he paid for it. How much money did the salesman make during these transactions?
10. On the blueprint, the scale indicates that 2 cm represents 5 ft. What are the actual dimensions of a room that is 4.8 cm by 6 cm on the blueprint?
Answer by JayJay_T(6)   (Show Source):
You can put this solution on YOUR website! 7. Suppose the amount of passengers boarding in Phoenix is 'x'. In Dallas we 've got the next amount: x - 1/2x + 4/5x (the original with amount with half of them leaving -1/2x and 4/5 of the original amount boarding). Let's call this new amount 'y'. In Memphis we are left with 3/4 of passengers:
1 - 3/4 = 1/4, but twice the amount of the remaining number boards: 1/4 + 2/4 = again 3/4. We now have 3/4y - passengers. Let's call this number 'z'
In Chicago 2/3 got off: z - 2/3z = 39, leaving 39 passengers.
Now we can calculate: 3/3z - 2/3z = 1/3z = 39 => z = 117.
If 'z' is 117, y = 4/3z (since 3/4y = z) = 156
We still have to find out about the original number 'x' => x - 1/2x + 4/5x = y = 156 =>
10x - 5x + 8x = 1560
13x = 1560
x = 120
8. 2 unknown variables here, the number of students 'x' and the number of cookies, 'y'. This should give us 2 equations, and indeed:
If we take from the total amount of cookies y a quantity equal to 3 pieces per student -3x, we end up with 5 cookies. If we do the same exercise with 4 cookies per student, we end up in debth, heating the cooker again for 2 more cookies.
y - 3x = 5
y - 4x = -2
Solving:
y + 2 = 4x
(y + 2)/4 = x
y - 3(y + 2)/4 = 5
y - 3/4y - 6/4 = 5
4y - 3y - 6 = 20
y = 26
Leaving us with x = 7
9. 4.327 - 2.500 = 1.827 profit
Buying a camper with 2/3th of 1.823 = 1.218 cost of the camper, leaving only 609 as profit.
Selling the camper for twice the price he paid (1.218) gives a return of 2.436, leaving again a profit of 1.218. Together with the first profit (609), the new amount of profit is $1.827.
10.
if 2cm equals 5ft, then 4.8 equals 5x2.4 = 12 and 6 equals 15, leaving us with a room of 180 square feet
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