Could someone please help me with Algebra?

Question

**Help me with these word problems they must be answered using equations.**

Sunset rents an SUV at $21.95 plus $0.23 per mile. Sunrise rents the same vehicle for $24.95 plus $0.19 per mile. For what mileage is the cost the same?

Six pears and three apples cost $3.90. Two pears and five apples cost $3.30. How much does one pear cost?

Two cars leave town going opposite directions. One car is traveling 55 mph, and the other is traveling 65 mph How long will it take before they are 180 miles apart?

A kayaker paddled 2 hours with a 6 mph current in a river. The return trip against the same current took 3 hours. Find the speed the kayaker would make in still water

Your piggy bank has 25 coins in it; some are quarters and some are nickels. You have $3.45. How many nickels do you have?

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?

This is no where near all of my homework try a packet of 16 pages!

Answer 1

For the first problem, set the two equations equal to each other. Solve for the number of miles.
$21.95 + $0.23 M = $24.95 + $0.19 M

For the second one, you must eliminate one of the variables.
6P + 3A = $3.90

2P + 5A = $ 3.30

Multiply the second equation by 3

6P + 15A = $9.90 Now, subtract the first equation from this. That will leave you with apples alone, Once you have the cost of an apple alone, you can easily substitute in and find the cost of a pear.

For the third one, add the two speeds, and divide the total milage by that number. This will give the time.

Let me know once you finish those and we’ll look at the others.

31 DEC 06, 2038 hrs, GMT.

Answer 2

Here's one of your questions; the rest are similar in method. You have to define your terms and set up your equation; and then plug in the numbers.

A kayaker paddled 2 hours with a 6 mph current in a river. The return trip against the same current took 3 hours. Find the speed the kayaker would make in still water

In this question, you have the kayak's speed, the current speed, the distance travelled and the time.

k = kayak speed (mph)
c = current speed (mph)
d = distance (miles)
t = time (h)

distance = time * speed
d = t * (k + c) going with the current
d = 2 * (k + 6)

d = t * (k - c) going against the current.
d = 3 * (k - 6)

(The actual distance is irrelevant.) Both equations have d on the left side, so the right sides must be equal.
2 * (k + 6) = 3 * (k - 6)
2k + 12 = 3k - 18
30 = k

So the kayak travels 30 mph in still water.

Similar steps (identifying your elements and setting up your equation) will work for all of these problems. Hope that helps; good luck.

Answer 3

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

s = number of student tickets sold
a = number of adult tickets sold
t = total number of tickets sold
R = receipts

s + a = t
2s + 3.5a = R

s + a = 1500
2s + 3.5a = 3825

Subtract twice the first equation from the second.
1.5a = 825
a = (2/3)(825) = 550
s = 1500 - a = 1500 - 550 = 950

950 students bought tickets.

Answer 4

Sunset rents an SUV at $21.95 plus $0.23 per mile. Sunrise rents the same vehicle for $24.95 plus $0.19 per mile. For what mileage is the cost the same?
Sunset: y= 21.95+0.23x
Sunrise: y= 24.95+.19x
Since you want to know when the mileage will cost the same and b/c it's an linear equation, set sunset and sunrise's equation equal to each other. Like this:
21.95+0.23x = 24.95+.19x
Solve for x.
if you get it right you should have 75 as x.

Answer 5

the apple pear problem

6 pears + 3 apples = 3.90
2 pears + 5 apples = 3.30

8 P + 8 A = 7.20

6P _ 3A = 3.90
-6P - 15A = - 9.90

- 12 A = - 6.00
12 A = 6.00

A = 6.00 divided by 12 = 50 cents for one apple

6 Pears + 3 apples cost 3.90

6 pears cost (3 x .50) = 3.90

6 pears cost 3.90 - 1.50 = 2.40

1 pear cost 2.40 divided by 6 = .40 cents

this can be proved by filling these amounts into the equations

Answer 6

Here is the pears and apples:
let p be the number of pears and a the number of apples.
Read the question and write the formulas:
6p + 3a = 3.90
2p + 5a = 3.30
Solve one of these equations for a.
plug it into the other equation where you see an "a".
Solve that equation for p.

Answer 7

I'll do the piggy bank one. He're the idea - if you get two equations and two unknowns, you can figure this out:

25 coins, nickels (n) and quarters (q)

n+q = 25

5n + 25q = 345

So, n = 25 -q

So, 5(25-q) + 25q = 345

Combining terms:

125 -5q + 25q = 345

20q = 220

q = 11
n=14

14 * .05 = .70
11 * 25 = 2.75

Answer 8

Hold on there! I'm not doing ALL your homework for you. If you want help with 1 or 2, fine, but this is WAY too much.