Asked by Bonk’s Joe 887 not an AI I think
Lila is laying a pass 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 one paver cost $1.49 each she only twice as many as two paver and a half and as many as paver three paver two cost $2.50 each Three pay for three cost $.75 which would be the best to buy
Answers
Answered by
GPT-4o mini
Let's break down the cost of each type of paver stone based on the quantities provided:
1. **Paver 1**: Costs $1.49 each.
2. **Paver 2**: Costs $2.50 each. Lila only needs half as many of Paver 2 compared to Paver 1.
3. **Paver 3**: Costs $.75 each. Lila needs twice as many Paver 3 as Paver 1.
Let’s use a variable \( x \) to represent the number of Paver 1 stones she buys.
- **Number of Paver 1**: \( x \)
- **Number of Paver 2**: Since Lila only needs half as many Paver 2 as Paver 1, the equation would be:
- \( \frac{x}{2} \)
- **Number of Paver 3**: Lila needs twice as many Paver 3 as Paver 1, so:
- \( 2x \)
Now we can calculate the total cost for each type of paver based on \( x \):
1. **Cost for Paver 1**:
\[
\text{Cost 1} = x \cdot 1.49
\]
2. **Cost for Paver 2**:
\[
\text{Cost 2} = \left(\frac{x}{2}\right) \cdot 2.50 = \frac{2.50x}{2} = 1.25x
\]
3. **Cost for Paver 3**:
\[
\text{Cost 3} = (2x) \cdot 0.75 = 1.50x
\]
Now we have the total costs expressed in terms of \( x \):
- **Cost for Paver 1**: \( 1.49x \)
- **Cost for Paver 2**: \( 1.25x \)
- **Cost for Paver 3**: \( 1.50x \)
To determine which is the best price, let's compare these costs:
- Paver 1: \( 1.49x \)
- Paver 2: \( 1.25x \) (cheapest)
- Paver 3: \( 1.50x \)
From this comparison, we can see that **Paver 2**, at $2.50 each, results in the lowest cost when considering the number of pavers Lila needs to buy.
Thus, the best paver to buy is **Paver 2**.
1. **Paver 1**: Costs $1.49 each.
2. **Paver 2**: Costs $2.50 each. Lila only needs half as many of Paver 2 compared to Paver 1.
3. **Paver 3**: Costs $.75 each. Lila needs twice as many Paver 3 as Paver 1.
Let’s use a variable \( x \) to represent the number of Paver 1 stones she buys.
- **Number of Paver 1**: \( x \)
- **Number of Paver 2**: Since Lila only needs half as many Paver 2 as Paver 1, the equation would be:
- \( \frac{x}{2} \)
- **Number of Paver 3**: Lila needs twice as many Paver 3 as Paver 1, so:
- \( 2x \)
Now we can calculate the total cost for each type of paver based on \( x \):
1. **Cost for Paver 1**:
\[
\text{Cost 1} = x \cdot 1.49
\]
2. **Cost for Paver 2**:
\[
\text{Cost 2} = \left(\frac{x}{2}\right) \cdot 2.50 = \frac{2.50x}{2} = 1.25x
\]
3. **Cost for Paver 3**:
\[
\text{Cost 3} = (2x) \cdot 0.75 = 1.50x
\]
Now we have the total costs expressed in terms of \( x \):
- **Cost for Paver 1**: \( 1.49x \)
- **Cost for Paver 2**: \( 1.25x \)
- **Cost for Paver 3**: \( 1.50x \)
To determine which is the best price, let's compare these costs:
- Paver 1: \( 1.49x \)
- Paver 2: \( 1.25x \) (cheapest)
- Paver 3: \( 1.50x \)
From this comparison, we can see that **Paver 2**, at $2.50 each, results in the lowest cost when considering the number of pavers Lila needs to buy.
Thus, the best paver to buy is **Paver 2**.
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