Question
Laila is laying a path down for a new driveway. The store has three types of paver stones that will work for her space. She needs to know which paver is the best price. Paver 1 costs $1.49 each, and she will need twice as many as paver 2 and half as many as paver 3. Paver 2 costs $2.50 each. Paver 3 costs $0.75. Which paver will be the best buy? Your answer should be a number.
To determine which paver is the best buy, we need to compare the total cost of each type of paver.
Let's denote the number of paver 1 as "x." Since Laila needs twice as many paver 2 as paver 1, the number of paver 2 needed is 2x. Additionally, she needs half as many paver 3 as paver 1, so the number of paver 3 needed is (1/2)x.
The total cost of paver 1 is 1.49x.
The total cost of paver 2 is 2.50 * 2x = 5x.
The total cost of paver 3 is 0.75 * (1/2)x = 0.375x.
To determine the best buy, we need to find the value of x that minimizes the cost. Since x represents the number of pavers, it should be a positive whole number.
To compare the total costs, we can calculate the costs for a few different values of x:
For x = 1:
Paver 1: 1.49 * 1 = $1.49
Paver 2: 5 * 1 = $5
Paver 3: 0.375 * 1 = $0.375
For x = 2:
Paver 1: 1.49 * 2 = $2.98
Paver 2: 5 * 2 = $10
Paver 3: 0.375 * 2 = $0.75
For x = 3:
Paver 1: 1.49 * 3 = $4.47
Paver 2: 5 * 3 = $15
Paver 3: 0.375 * 3 = $1.125
Based on these calculations, it can be observed that the cost of paver 3 increases more rapidly compared to paver 1 and paver 2. Therefore, as x increases, the difference in cost between paver 3 and the others will continue to grow. For larger values of x, paver 3 will become the most expensive option.
Therefore, to minimize the cost, the best buy is paver 1, which costs $1.49 each.
wrong
I apologize for the mistake. Let's correct the calculation.
Let's denote the number of paver 1 as "x." Since Laila needs twice as many paver 2 as paver 1, the number of paver 2 needed is 2x. Additionally, she needs half as many paver 3 as paver 1, so the number of paver 3 needed is (1/2)x.
The total cost of paver 1 is 1.49 * x = 1.49x.
The total cost of paver 2 is 2.50 * 2x = 5x.
The total cost of paver 3 is 0.75 * (1/2)x = 0.375x.
To determine the best buy, we need to compare these costs.
For each paver type:
- Paver 1: 1.49x
- Paver 2: 5x
- Paver 3: 0.375x
To find the lowest cost, we need to compare the values when x is a positive whole number.
Let's calculate the costs for a few different values of x:
For x = 1:
Paver 1: 1.49 * 1 = $1.49
Paver 2: 5 * 1 = $5
Paver 3: 0.375 * 1 = $0.375
For x = 2:
Paver 1: 1.49 * 2 = $2.98
Paver 2: 5 * 2 = $10
Paver 3: 0.375 * 2 = $0.75
For x = 3:
Paver 1: 1.49 * 3 = $4.47
Paver 2: 5 * 3 = $15
Paver 3: 0.375 * 3 = $1.125
Based on these calculations, when x = 1, paver 1 is the lowest cost option. Therefore, paver 1, which costs $1.49 each, is the best buy.