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Answer :
To find out how much Emily spent on cappuccinos and scones over the last two weeks, we need to evaluate each expression. Let's understand step by step:
1. Understanding the Problem:
- Emily buys cappuccinos and scones for a book club. Each cappuccino costs [tex]$c$[/tex] dollars, and each scone costs [tex]$s$[/tex] dollars.
- The number of people who attended the book club were 12 last week and 15 this week.
- We need to determine how much Emily spent over the two weeks combined.
2. Analyzing the Expressions:
- Expression 1: [tex]\(27c + 27s\)[/tex]
- This implies that Emily spent on 27 cappuccinos and 27 scones. This doesn't break down the cost per each week distinctly, but if we think about it, it could represent the total over both weeks. This would be the sum of participants from both weeks (12 + 15 = 27), multiplied by the cost of one cappuccino and one scone.
- Expression 2: [tex]\(12(c + s) + 15(c + s)\)[/tex]
- This expression separates the cost for each week. For the first week, 12 people came, so the total cost was [tex]\(12 \times (c + s)\)[/tex]. For the second week, 15 people came, so the cost was [tex]\(15 \times (c + s)\)[/tex]. Adding these together would give us the total for both weeks.
- Expression 3: [tex]\(54(c + s)\)[/tex]
- This implies that she spent money such that 54 instances of (c + s) were bought, which doesn't accurately represent the number of participants from both weeks (27 in total). Thus, this expression doesn't align with what happened over the two weeks.
- Expression 4: [tex]\(12c + 12s + 15c + 15s\)[/tex]
- This expression appears to also separate the cost for each week. For the first week, the cost is [tex]\(12c + 12s\)[/tex], and for the second week, it is [tex]\(15c + 15s\)[/tex]. When we add these together, we have the total cost for both weeks.
3. Verifying the Correct Expressions:
Based on the analysis, the expressions that correctly represent how much Emily spent over the past two weeks are:
- [tex]\(12(c + s) + 15(c + s)\)[/tex]
- [tex]\(12c + 12s + 15c + 15s\)[/tex]
These expressions both break down the costs week by week and add them correctly for a total cost across two weeks.
So, the correct expressions that represent how much Emily spent the past two weeks are:
- [tex]\(12(c + s) + 15(c + s)\)[/tex]
- [tex]\(12c + 12s + 15c + 15s\)[/tex]
We have carefully verified that these expressions match the context described in the problem, and they faithfully account for Emily's total spending over the two weeks.
1. Understanding the Problem:
- Emily buys cappuccinos and scones for a book club. Each cappuccino costs [tex]$c$[/tex] dollars, and each scone costs [tex]$s$[/tex] dollars.
- The number of people who attended the book club were 12 last week and 15 this week.
- We need to determine how much Emily spent over the two weeks combined.
2. Analyzing the Expressions:
- Expression 1: [tex]\(27c + 27s\)[/tex]
- This implies that Emily spent on 27 cappuccinos and 27 scones. This doesn't break down the cost per each week distinctly, but if we think about it, it could represent the total over both weeks. This would be the sum of participants from both weeks (12 + 15 = 27), multiplied by the cost of one cappuccino and one scone.
- Expression 2: [tex]\(12(c + s) + 15(c + s)\)[/tex]
- This expression separates the cost for each week. For the first week, 12 people came, so the total cost was [tex]\(12 \times (c + s)\)[/tex]. For the second week, 15 people came, so the cost was [tex]\(15 \times (c + s)\)[/tex]. Adding these together would give us the total for both weeks.
- Expression 3: [tex]\(54(c + s)\)[/tex]
- This implies that she spent money such that 54 instances of (c + s) were bought, which doesn't accurately represent the number of participants from both weeks (27 in total). Thus, this expression doesn't align with what happened over the two weeks.
- Expression 4: [tex]\(12c + 12s + 15c + 15s\)[/tex]
- This expression appears to also separate the cost for each week. For the first week, the cost is [tex]\(12c + 12s\)[/tex], and for the second week, it is [tex]\(15c + 15s\)[/tex]. When we add these together, we have the total cost for both weeks.
3. Verifying the Correct Expressions:
Based on the analysis, the expressions that correctly represent how much Emily spent over the past two weeks are:
- [tex]\(12(c + s) + 15(c + s)\)[/tex]
- [tex]\(12c + 12s + 15c + 15s\)[/tex]
These expressions both break down the costs week by week and add them correctly for a total cost across two weeks.
So, the correct expressions that represent how much Emily spent the past two weeks are:
- [tex]\(12(c + s) + 15(c + s)\)[/tex]
- [tex]\(12c + 12s + 15c + 15s\)[/tex]
We have carefully verified that these expressions match the context described in the problem, and they faithfully account for Emily's total spending over the two weeks.
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