Please and thank you?

Question

1. Six pears and three apples cost $3.90. Two pears and five apples cost $3.30. How much does one pear cost? Hint: You have two unknowns (variables), so you need two equations. Write one equation for each situation and solve the system of equations.

Let p = the cost of one pear

Let a = the cost of one apple

a. Write a system of equations that can be used to determine the cost of pears and apples.

b. Determine the cost of one pear and one apple. Use mathematics to explain how you determined your answer.


2. There were 1500 people at a high school football game. Student tickets were $2.00 and adult tickets were $3.50. The total receipts for the game were $3825. How many students bought tickets?

Let a = the number of adult tickets purchased.

Let s = the number of student tickets purchased.

a. Write a system of equations that can be used to determine the number of adult and student tickets purchased.

b. Determine the number of adults tickets sold and the number of student tickets sold. Use mathematics to explain how you determined your answer.


3. An airplane flew 4 hours with a 25 mph tail wind. The return trip against the same wind took 5 hours. Find the speed of the airplane in still air. This similar to the current problem as you have to consider the 25 mph tailwind and headwind.
Let r = the rate or speed of the airplane in still air.

Let d = the distance

a. Write a system of equations for the airplane. One equation will be for the outbound trip with tailwind of 25 mph. The second equation will be for the return trip with headwind of 25 mph.

b. Solve the system of equations for the speed of the airplane in still air.


4. Your family likes to go to baseball games. At one game your family bought 5 soft drinks and 5 hot dogs for $22.25. At the next game your family attended they bought 4 soft drinks and 3 hot dogs for $14.50. What is the cost of one soft drink and one hot dog?

Let s = the cost of one soft drink

Let h = the cost of one hot dog

a. Write a system of equations modeling the situation described above.

b. Solve the system for the cost of one soft drink + one hot dog. (You will have to add your solutions together for this one.)


5. Suppose you just have just enough dimes and quarters to pay for a loaf of bread and quart of milk, which cost $3.45. You have a total of 15 dimes and quarters.

Let d = the number of dimes you have.

Let q = the number of quarters you have.

a. Write a system of equations that models the information given above.

b. Solve the system for the number of dimes and quarters you have. You may want to solve this by graphing.

Answer 1

1.)
6p + 3a = 390
2p + 5a = 330
Divide equation 1 by 3:
2p + a = 130
Subtract from equation 2:
4a = 200, a = 50
1 Apple is 50 cents.
Substitute in equation 2:
2p + 5(50) = 330
2p = 330 - 250 = 80
1 Pear is 40 cents.
Substitute in equation 1:
6(40) + 3(50) = 390
240 + 150 = 390
LHS = RHS

Answer 2

1. 6p + 3a = 390 --> a = (390 - 6p)/3 = 130 - 2p
... 2p + 5a = 330 --> 2p + 5(130 - 2p) = 330
................ ................. 2p + 650 - 10p = 330

Surely you can get the rest from there?


2. a + s = 1500 --> a = 1500 - s
... 2a + 3.5s = 3825 --> 2(1500 - s) + 3.5s = 3825
................... ............... 3000 - 2s + 3.5s = 3825

Ditto


4. 5s + 5h = 22.25 --> h = (22.25 - 5s)/5 = 4.45 - s
... 4s + 3h = 14.5 --> 4s + 3(4.45 - s) = 14.5
.............. .................4s + 13.35 - 3s = 14.5

Do you understand how these work now?


5. Same as the others