Hi, I am having some trouble with some problems, can you please help. thanxs!!!
1. A car rental agency charges $250 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $300?
-Would the equation look like: 300= 250x + .25 ?
6. A train ticket in a certain city is $2.50. People who use the train also have the option of purchasing a frequent rider pass for $18.00 each month. With the pass, each ticket costs only $1.75. Determine the number of times in a month the train must be used so that total monthly cost without the pass is the same as the total month cost with the pass?
-Would the equation look like: 2.50 = 18.00x + 1.75?
20. A bookcase is to be constructed. The height of the bookcase is 4 feet longer than the lenght of a shelf. If 20 feet of lumber is available for the entire unit (including the shelves, but NOT the back of the bookcase), find the length and height of the unit.
-Would the equation be: 4x + y=20
x being the length, and y being length of the shelf.
26. Inclusive of a 7.2% sales tax, a diamond ring sold for $2358.40. Find the price of the ring before the tax was added. (Round to the nearest cent, if necessary)
-This one I don't understand.
30. There are 16 more sophmores than juniors in an 8AM algebra class. If there are 54 students in this class, find the number of sophmores and the number of juniors?
-This one I am not too sure how to do it.
45. The sum of the anlges of a triangle is 180 degrees. Find the three angles of the triangle if one angle is four times the smallest angle and the third angle is 24 degrees greater than the smallest angle.
-This one I don't understand.
. A car rental agency charges $250 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $300?
-Would the equation look like: 300= 250x + .25 ?
Wouldn't it be something like this.
$300 total cost - weekly rental (250) = $50 remaining. Then how many miles can be driven to use $50 at 0.25/mile? That would be $50 = miles driven x 0.25/mile
or to put it all together---
300-250 = 0.25x and solve for x.
6. A train ticket in a certain city is $2.50. People who use the train also have the option of purchasing a frequent rider pass for $18.00 each month. With the pass, each ticket costs only $1.75. Determine the number of times in a month the train must be used so that total monthly cost without the pass is the same as the total month cost with the pass?
Let's say the number of days we ride the train is x. Then
cost to ride train on daily basis = 2.50 per day times number of days or
2.50x.
cost to ride train if we purchase frequent rider pass for 18.00 is
1.75x + 18.
We want the cost of each to be the same; therefore, set them equal to each other.
2.50x = 1.75x + 18
solve for x. I obtained 24 days
26. Inclusive of a 7.2% sales tax, a diamond ring sold for $2358.40. Find the price of the ring before the tax was added. (Round to the nearest cent, if necessary)
Let's call the initial cost of the ring x.
So cost of ring + (cost of ring* 7.2% tax) = total cost.
x + 0.072x = 2358.40
solve for x. I found x to be $2200.00
Check my thinking.
30. There are 16 more sophmores than juniors in an 8AM algebra class. If there are 54 students in this class, find the number of sophmores and the number of juniors?
Do you know how to solve equations simultaneously? If so here is how you set it up?
Let s = # sophomores (note the correct spelling of sophomore).
Let j = # juniors. The two equations are
(1)    s + j = 54 and
(2)    s = j + 16
Solving those I found s = 35 and j = 19
Check my work.
45. The sum of the anlges of a triangle is 180 degrees. Find the three angles of the triangle if one angle is four times the smallest angle and the third angle is 24 degrees greater than the smallest angle.
Let's call the smallest angle S.
Then 4S is one angle and
S+24 is the next one. All of these must add to 180; therefore,
S + 4S + S+24 = 180
solve for S. I found S to be 26 degrees. then 4S = 4*26 = ?? and
S + 24 = ??
Check my thinking. Check my work.
For the car rental problem, the equation would actually be:
300 = 250 + 0.25x
To solve for x, you would subtract 250 from both sides of the equation:
300 - 250 = 0.25x
50 = 0.25x
Then, divide both sides of the equation by 0.25:
50/0.25 = x
x = 200
So, you can travel 200 miles in one week for $300.
For the train ticket problem, the equation would be:
2.50x = 1.75x + 18
To solve for x, you would subtract 1.75x from both sides of the equation:
2.50x - 1.75x = 18
0.75x = 18
Then, divide both sides of the equation by 0.75:
18/0.75 = x
x = 24
So, the train must be used 24 times in a month for the total monthly cost without the pass to be the same as the total monthly cost with the pass.
For the bookcase problem, the equation would be:
x + x + 4 = 20
To solve for x, you would subtract 4 from both sides of the equation:
2x = 16
Then, divide both sides of the equation by 2:
x = 8
So, the length of the unit is 8 feet and the height is 12 feet.
For the diamond ring problem, the equation would be:
1.072x = 2358.40
To solve for x, you would divide both sides of the equation by 1.072:
x = 2358.40/1.072
x ≈ 2197.56
So, the price of the ring before the tax was added is approximately $2197.56.
For the algebra class problem, you can set up a system of equations:
s + j = 54
s = j + 16
To solve for s and j, you can substitute the second equation into the first equation:
j + 16 + j = 54
2j + 16 = 54
Subtract 16 from both sides of the equation:
2j = 38
Divide both sides of the equation by 2:
j = 19
Substitute the value of j back into the second equation to solve for s:
s = 19 + 16
s = 35
So, there are 35 sophomores and 19 juniors in the algebra class.
For the triangle angle problem, you can set up the equation:
S + 4S + S + 24 = 180
To solve for S, you would combine like terms:
6S + 24 = 180
Subtract 24 from both sides of the equation:
6S = 156
Divide both sides of the equation by 6:
S = 26
Then, you can find the other angles:
4S = 4(26) = 104
S + 24 = 26 + 24 = 50
So, the three angles of the triangle are 26 degrees, 104 degrees, and 50 degrees.