Black Diamond Ski Resort charges $25 for ski rental and $10 an hour to ski. Bunny Hill Ski Resort charges $50 for ski rental and $5 an hour to ski. Create an equation to determine at what point the cost of both ski slopes is the same.
a. 10x + 25 = 5x + 50
b. 10x − 25 = 5x − 50
c. 10x + 50 = 5x + 25
d. 10x − 50 = 5x − 25
a. 10x + 25 = 5x + 50 (This equation represents the total cost of skiing at Black Diamond and Bunny Hill. 10x represents the cost per hour of skiing at Black Diamond and 5x represents the cost per hour of skiing at Bunny Hill. The constants 25 and 50 represent the costs of rental at Black Diamond and Bunny Hill respectively.)
To solve for x:
10x + 25 = 5x + 50
10x - 5x = 50 - 25
5x = 25
x = 5
Therefore, at 5 hours of skiing, the cost of skiing at both slopes is the same.
Carolina biked 1 mile more than twice the number of miles James biked. Carolina biked a total of 5 miles. Write an equation to determine how many miles James biked.
a. x − 1 = 2(5)
b. x over five = 2(1)
c. 5 + 2x = 1
d. 5 = 2x + 1
a. x − 1 = 2(5) (This equation represents Carolina biking 1 mile more than twice the number of miles James biked. 'x' represents the number of miles James biked.)
To solve for x:
x - 1 = 2(5)
x - 1 = 10
x = 11
Therefore, James biked 11 miles.
The temperature in San Diego, California, is 5 degrees warmer than twice the temperature in Boise, Idaho. The temperature in San Diego is 61 degrees. Write an equation to determine the temperature in Boise.
2x − 5 = 61
2x − 61 = 5
2x + 61 = 5
2x + 5 = 61
To determine at what point the cost of both ski slopes is the same, we need to equate the total cost for each ski resort.
Let's use the variable x to represent the number of hours of skiing.
For Black Diamond Ski Resort, the total cost is given by:
Total cost for Black Diamond = Ski rental cost + (Skiing cost per hour * Number of hours)
Total cost for Black Diamond = 25 + 10x
For Bunny Hill Ski Resort, the total cost is given by:
Total cost for Bunny Hill = Ski rental cost + (Skiing cost per hour * Number of hours)
Total cost for Bunny Hill = 50 + 5x
To find the point where the cost is the same, we equate the two equations:
25 + 10x = 50 + 5x
Simplifying the equation, we get:
5x - 5x = 50 - 25
5x = 25
Dividing both sides of the equation by 5, we find:
x = 5
Therefore, the correct equation to determine at what point the cost of both ski slopes is the same is:
c. 10x + 50 = 5x + 25
To determine at what point the cost of both ski slopes is the same, we need to set up an equation.
Let's assume the variable x represents the number of hours spent skiing.
For Black Diamond Ski Resort:
The cost of ski rental is $25.
The cost of skiing per hour is $10.
So the equation for the cost of skiing at Black Diamond Ski Resort is:
10x + 25
For Bunny Hill Ski Resort:
The cost of ski rental is $50.
The cost of skiing per hour is $5.
So the equation for the cost of skiing at Bunny Hill Ski Resort is:
5x + 50
To find at what point the cost of both ski slopes is the same, we need to set the two equations equal to each other:
10x + 25 = 5x + 50
Therefore, the correct equation to determine at what point the cost of both ski slopes is the same is:
a. 10x + 25 = 5x + 50