Solve this: the cost of renting a kayak for 1 hour is $15, for 2 hours is $20, for 3 hours is $25, for 4 hours is $30. Write two different algebraic expressions that can be used to find the cost of renting a kayak for h hours.
one expression is
10+5h
To find the cost of renting a kayak for h hours, we can use two different algebraic expressions:
1. Expression using the "if-then" logic:
Let's break down the given information:
- The cost for renting a kayak for 1 hour is $15.
- The cost for renting a kayak for 2 hours is $20, which is $5 more than renting for 1 hour.
- The cost for renting a kayak for 3 hours is $25, which is $5 more than renting for 2 hours.
- The cost for renting a kayak for 4 hours is $30, which is $5 more than renting for 3 hours.
From the pattern observed, we can conclude that for each additional hour, the cost increases by $5.
Therefore, we can use the following algebraic expression:
Cost = $15 + ($5 × (h - 1))
2. Expression using linear equations:
We can also consider the given cost values as points on a coordinate grid, where the x-axis represents the number of hours (h) and the y-axis represents the cost.
The points are as follows:
(1, 15)
(2, 20)
(3, 25)
(4, 30)
To find the equation of the line passing through these points, we can use the slope-intercept form of a linear equation: y = mx + b.
Using the formula for finding the slope:
slope (m) = (change in y) / (change in x)
= (y2 - y1) / (x2 - x1)
= (20 - 15) / (2 - 1)
= 5
Substituting the slope (m) and the coordinates of one point (1, 15) into the slope-intercept form, we get:
y = 5x + b
15 = 5(1) + b
15 = 5 + b
Solving for b, we find b = 10.
Therefore, the equation for the line passing through the given points is:
Cost = 5h + 10
To find the cost of renting a kayak for h hours, we need to determine the pattern in the given cost values.
From the information provided, we can observe that the cost increases by $5 for each additional hour beyond the first hour. Therefore, the cost of renting a kayak can be represented by two different algebraic expressions:
1. Expression using the number of hours:
If we let x represent the number of hours, the cost of renting a kayak can be expressed as:
- For 1 hour, the cost is $15: C = 15
- For each additional hour, the cost increases by $5: C = 15 + 5(x - 1) = 15 + 5x - 5 = 5x + 10
2. Expression using the number of additional hours:
If we let y represent the number of additional hours beyond the first hour, the cost of renting a kayak can be expressed as:
- The cost for the first hour is $15: C = 15
- The cost for each additional hour beyond the first hour increases by $5: C = 15 + 5y
Both expressions will yield the same result when evaluated for a given value of hours, whether it is given as the total number of hours or as the number of additional hours beyond the first hour.