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Answer :
To understand how much Greta spent on cappuccinos and scones for her book club over the past two weeks, let's break down each part of the problem.
In the first week, 12 people attended the book club:
- Each person had a cappuccino and a scone.
- Therefore, the cost for each person was [tex]\( c + s \)[/tex].
- For 12 people, the total cost was [tex]\( 12 \times (c + s) \)[/tex].
In the second week, 15 people attended:
- Similarly, each person had a cappuccino and a scone.
- The total cost for 15 people was [tex]\( 15 \times (c + s) \)[/tex].
To find the total cost over both weeks, we add the costs from both weeks:
[tex]\[ 12(c + s) + 15(c + s) \][/tex]
Now let's go through the expressions to see which ones match the total cost:
1. Expression: [tex]\( 27c + 27s \)[/tex]
- This represents a total of 27 cappuccinos and 27 scones. This matches because [tex]\( 12 + 15 = 27 \)[/tex] (12 from the first week and 15 from the second week).
2. Expression: [tex]\( 12(c + s) + 15(c + s) \)[/tex]
- This directly sums up the costs from each week as calculated above, so it matches exactly.
3. Expression: [tex]\( 54(c + s) \)[/tex]
- This suggests that 54 cappuccinos and 54 scones were purchased in total, which is incorrect because Greta actually bought 27 cappuccinos and 27 scones.
4. Expression: [tex]\( 12c + 12s + 15c + 15s \)[/tex]
- This separates the costs of cappuccinos and scones but still matches because it calculates as [tex]\( (12 + 15)c + (12 + 15)s \)[/tex] which equals [tex]\( 27c + 27s \)[/tex].
So, the correct expressions that represent how much Greta spent over the past two weeks are [tex]\( 27c + 27s \)[/tex], [tex]\( 12(c + s) + 15(c + s) \)[/tex], and [tex]\( 12c + 12s + 15c + 15s \)[/tex]. These expressions correctly reflect the total cost of all items purchased.
In the first week, 12 people attended the book club:
- Each person had a cappuccino and a scone.
- Therefore, the cost for each person was [tex]\( c + s \)[/tex].
- For 12 people, the total cost was [tex]\( 12 \times (c + s) \)[/tex].
In the second week, 15 people attended:
- Similarly, each person had a cappuccino and a scone.
- The total cost for 15 people was [tex]\( 15 \times (c + s) \)[/tex].
To find the total cost over both weeks, we add the costs from both weeks:
[tex]\[ 12(c + s) + 15(c + s) \][/tex]
Now let's go through the expressions to see which ones match the total cost:
1. Expression: [tex]\( 27c + 27s \)[/tex]
- This represents a total of 27 cappuccinos and 27 scones. This matches because [tex]\( 12 + 15 = 27 \)[/tex] (12 from the first week and 15 from the second week).
2. Expression: [tex]\( 12(c + s) + 15(c + s) \)[/tex]
- This directly sums up the costs from each week as calculated above, so it matches exactly.
3. Expression: [tex]\( 54(c + s) \)[/tex]
- This suggests that 54 cappuccinos and 54 scones were purchased in total, which is incorrect because Greta actually bought 27 cappuccinos and 27 scones.
4. Expression: [tex]\( 12c + 12s + 15c + 15s \)[/tex]
- This separates the costs of cappuccinos and scones but still matches because it calculates as [tex]\( (12 + 15)c + (12 + 15)s \)[/tex] which equals [tex]\( 27c + 27s \)[/tex].
So, the correct expressions that represent how much Greta spent over the past two weeks are [tex]\( 27c + 27s \)[/tex], [tex]\( 12(c + s) + 15(c + s) \)[/tex], and [tex]\( 12c + 12s + 15c + 15s \)[/tex]. These expressions correctly reflect the total cost of all items purchased.
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