ricardo runs act tutoring camps he used to hold three sessions at 50$ per session but recently changed his buisness plan now each camp consists of sux sessions at 34$ per session how much money will he make per camo under his new buissnes plan use the diffrence of two squares find the amount

Answer 1

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.

1. Old Business Plan:

   • Number of sessions: 3
   • Price per session: $50
   • Total revenue from one camp: $$3\text{ sessions}\times 50\text{ dollars/session}=150\text{ dollars}$$

2. New Business Plan:

   • Number of sessions: 6
   • Price per session: $34
   • Total revenue from one camp: $$6\text{ sessions}\times 34\text{ dollars/session}=204\text{ dollars}$$

3. 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.