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.