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Answer :
To determine how much Shelby spent on cappuccinos and scones over the past two weeks, we will consider both weeks individually and then combine the totals.
1. Understanding the scenario:
- Last week there were 12 people, and Shelby bought cappuccinos and scones for each person.
- This week there were 15 people, and again, Shelby bought cappuccinos and scones for each person.
2. Cost expressions:
- For one person, the total cost of a cappuccino and a scone is `(c + s)` dollars.
3. Calculating for each week:
- Last Week:
- Total people = 12
- Total cost last week = 12 times the cost of `(c + s)`, which is `12(c + s)`.
- This Week:
- Total people = 15
- Total cost this week = 15 times the cost of `(c + s)`, which is `15(c + s)`.
4. Total for both weeks:
- We add the costs of both weeks together:
- `12(c + s) + 15(c + s)`.
5. Combine and simplify:
- Combine the two expressions:
- `12(c + s) + 15(c + s)` simplifies to `(12 + 15)(c + s)`, which equals `27(c + s)`.
6. Checking the choices:
- [tex]$27c + 27s$[/tex] represents the total cost by expanding `27(c + s)` to `27c + 27s`.
- [tex]$12(c+s) + 15(c+s)$[/tex] adds the two weekly costs, which simplifies to `27(c + s)`.
- [tex]$54(c+s)$[/tex] is incorrect because `54` does not represent the total number of people (which is `27`).
- [tex]$12c + 12s + 15c + 15s$[/tex] is another way to write `27c + 27s`, aligning with the expanded version.
Therefore, the correct expressions that represent how much Shelby spent the past two weeks are:
- [tex]$27c + 27s$[/tex]
- [tex]$12(c+s) + 15(c+s)$[/tex]
- [tex]$12c + 12s + 15c + 15s$[/tex]
1. Understanding the scenario:
- Last week there were 12 people, and Shelby bought cappuccinos and scones for each person.
- This week there were 15 people, and again, Shelby bought cappuccinos and scones for each person.
2. Cost expressions:
- For one person, the total cost of a cappuccino and a scone is `(c + s)` dollars.
3. Calculating for each week:
- Last Week:
- Total people = 12
- Total cost last week = 12 times the cost of `(c + s)`, which is `12(c + s)`.
- This Week:
- Total people = 15
- Total cost this week = 15 times the cost of `(c + s)`, which is `15(c + s)`.
4. Total for both weeks:
- We add the costs of both weeks together:
- `12(c + s) + 15(c + s)`.
5. Combine and simplify:
- Combine the two expressions:
- `12(c + s) + 15(c + s)` simplifies to `(12 + 15)(c + s)`, which equals `27(c + s)`.
6. Checking the choices:
- [tex]$27c + 27s$[/tex] represents the total cost by expanding `27(c + s)` to `27c + 27s`.
- [tex]$12(c+s) + 15(c+s)$[/tex] adds the two weekly costs, which simplifies to `27(c + s)`.
- [tex]$54(c+s)$[/tex] is incorrect because `54` does not represent the total number of people (which is `27`).
- [tex]$12c + 12s + 15c + 15s$[/tex] is another way to write `27c + 27s`, aligning with the expanded version.
Therefore, the correct expressions that represent how much Shelby spent the past two weeks are:
- [tex]$27c + 27s$[/tex]
- [tex]$12(c+s) + 15(c+s)$[/tex]
- [tex]$12c + 12s + 15c + 15s$[/tex]
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