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Answer :
To determine how much Kiera spent over the past two weeks on cappuccinos and scones for her book club, let's break down the problem step by step.
1. Identify the Costs and Number of People:
- Each cappuccino costs [tex]$c$[/tex] dollars.
- Each scone costs [tex]$s$[/tex] dollars.
- There were 12 people last week.
- There were 15 people this week.
2. Calculate the Total Costs:
- For last week, with 12 people, each person gets a cappuccino and a scone. So the cost for last week is:
[tex]\[
12(c + s)
\][/tex]
- For this week, with 15 people, each person also gets a cappuccino and a scone. So the cost for this week is:
[tex]\[
15(c + s)
\][/tex]
3. Combine the Two Week's Costs:
- Add both weeks together to get the total cost for both weeks:
[tex]\[
12(c + s) + 15(c + s)
\][/tex]
- This expression can be expanded by distributing:
[tex]\[
12c + 12s + 15c + 15s
\][/tex]
4. Simplify the Total Expression:
- Combine like terms:
[tex]\[
(12c + 15c) + (12s + 15s) = 27c + 27s
\][/tex]
5. Select the Correct Expressions:
- Based on the breakdown, the expressions that accurately represent the total amount Kiera spent over the two weeks are:
- [tex]\( 12(c+s) + 15(c+s) \)[/tex]
- [tex]\( 12c + 12s + 15c + 15s \)[/tex]
- [tex]\( 27c + 27s \)[/tex]
Thus, the correct expressions from the options given are:
- [tex]\( 27c + 27s \)[/tex]
- [tex]\( 12(c+s) + 15(c+s) \)[/tex]
- [tex]\( 12c + 12s + 15c + 15s \)[/tex]
All of these expressions accurately reflect the total spending over the two weeks on cappuccinos and scones.
1. Identify the Costs and Number of People:
- Each cappuccino costs [tex]$c$[/tex] dollars.
- Each scone costs [tex]$s$[/tex] dollars.
- There were 12 people last week.
- There were 15 people this week.
2. Calculate the Total Costs:
- For last week, with 12 people, each person gets a cappuccino and a scone. So the cost for last week is:
[tex]\[
12(c + s)
\][/tex]
- For this week, with 15 people, each person also gets a cappuccino and a scone. So the cost for this week is:
[tex]\[
15(c + s)
\][/tex]
3. Combine the Two Week's Costs:
- Add both weeks together to get the total cost for both weeks:
[tex]\[
12(c + s) + 15(c + s)
\][/tex]
- This expression can be expanded by distributing:
[tex]\[
12c + 12s + 15c + 15s
\][/tex]
4. Simplify the Total Expression:
- Combine like terms:
[tex]\[
(12c + 15c) + (12s + 15s) = 27c + 27s
\][/tex]
5. Select the Correct Expressions:
- Based on the breakdown, the expressions that accurately represent the total amount Kiera spent over the two weeks are:
- [tex]\( 12(c+s) + 15(c+s) \)[/tex]
- [tex]\( 12c + 12s + 15c + 15s \)[/tex]
- [tex]\( 27c + 27s \)[/tex]
Thus, the correct expressions from the options given are:
- [tex]\( 27c + 27s \)[/tex]
- [tex]\( 12(c+s) + 15(c+s) \)[/tex]
- [tex]\( 12c + 12s + 15c + 15s \)[/tex]
All of these expressions accurately reflect the total spending over the two weeks on cappuccinos and scones.
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