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Maggie hosts a weekly book club and buys cappuccinos and scones for each person in the group. The cappuccinos cost [tex]$c$[/tex] dollars each, and the scones cost [tex]$s$[/tex] dollars each. There were 12 people who came to the book club last week and 15 people who came to the book club this week.

Pick all the expressions that represent how much Maggie spent the past two weeks:

A. [tex]27c + 27s[/tex]

B. [tex]12(c + s) + 15(c + s)[/tex]

C. [tex]54(c + s)[/tex]

D. [tex]12c + 12s + 15c + 15s[/tex]

Answer :

To find out how much Maggie spent over the past two weeks, we need to calculate her expenses for each week and then add them together.

1. For the first week:
- 12 people attended.
- Each person had a cappuccino costing [tex]$c$[/tex] and a scone costing [tex]$s$[/tex].
- The cost for one person is [tex]\( c + s \)[/tex].
- Total cost for the first week: [tex]\( 12 \times (c + s) \)[/tex].

2. For the second week:
- 15 people attended.
- Each person had a cappuccino costing [tex]$c$[/tex] and a scone costing [tex]$s$[/tex].
- Total cost for the second week: [tex]\( 15 \times (c + s) \)[/tex].

3. Total spending for both weeks:
- Add the expenses from both weeks:
[tex]\[
12 \times (c + s) + 15 \times (c + s)
\][/tex]
- Simplify the expression by factoring out [tex]\( (c + s) \)[/tex]:
[tex]\[
(12 + 15) \times (c + s) = 27 \times (c + s)
\][/tex]

Let's look at the provided choices and identify which of them represent this total:

- [tex]\( 27c + 27s \)[/tex]: This simplifies to the same expression if expanded: [tex]\( 27 \times (c + s) \)[/tex].

- [tex]\( 12(c+s) + 15(c+s) \)[/tex]: This matches our calculation exactly and also simplifies to [tex]\( 27 \times (c + s) \)[/tex].

- [tex]\( 54(c+s) \)[/tex]: This does not match, as it suggests twice the amount calculated.

- [tex]\( 12c + 12s + 15c + 15s \)[/tex]: This can be rewritten as [tex]\( (12c + 15c) + (12s + 15s) = 27c + 27s \)[/tex], which simplifies to [tex]\( 27 \times (c + s) \)[/tex].

Therefore, the expressions that represent how much Maggie spent are:
- [tex]\( 27c + 27s \)[/tex]
- [tex]\( 12(c+s) + 15(c+s) \)[/tex]
- [tex]\( 12c + 12s + 15c + 15s \)[/tex]

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