Question

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

Answer 1

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.

Answer 2

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

Answer 3

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.

Answer 4

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