To find the amount of money Ricardo will make per camp under his new business plan, we can first calculate the total revenue he generates from one camp for both the old and new plans and then analyze the difference using the difference of squares method.
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Old Business Plan:
- Number of sessions: 3
- Price per session: $50
- Total revenue from one camp: \[ 3 \text{ sessions} \times 50 \text{ dollars/session} = 150 \text{ dollars} \]
-
New Business Plan:
- Number of sessions: 6
- Price per session: $34
- Total revenue from one camp: \[ 6 \text{ sessions} \times 34 \text{ dollars/session} = 204 \text{ dollars} \]
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Difference in Revenue:
- The difference in revenue between the new and old business plans: \[ 204 \text{ dollars} - 150 \text{ dollars} = 54 \text{ dollars} \]
Using the Difference of Squares
The difference of squares method can be stated as: \[ a^2 - b^2 = (a - b)(a + b) \] For this scenario:
- Let \( a = 204 \) (new revenue)
- Let \( b = 150 \) (old revenue)
Calculating:
\[ 204^2 - 150^2 = (204 - 150)(204 + 150) \] Calculating the two components:
- \( 204 - 150 = 54 \)
- \( 204 + 150 = 354 \)
Then, using those values: \[ 204^2 - 150^2 = 54 \times 354 \]
Calculating \( 54 \times 354 \): \[ 54 \times 354 = 19026 \]
Though it shows a mathematical relationship, to find the revenue from new camp directly, just use the total revenue calculated separately:
- Ricardo would earn \( 204 \) dollars per camp under the new plan.
Thus, the final answers are:
- Under the new business plan, he makes $204 per camp.
- The difference from the previous revenue is $54.