I need help with a math problem

Mathematics
Tutor: None Selected Time limit: 1 Day

  Picture This earned $3,250 the first year.  Sally video taped 40 events.  She charged $100 for weddings, $75 for birthday parties, and $50 for graduations.  Sally video taped as many weddings as birthday parties and graduations combined.  Find the number of weddings, birthday parties, and graduations Sally video taped.

**Please show your work**

Dec 1st, 2015

Thank you for the opportunity to help you with your question!

Total number of events = 40

Let the number of birthday parties be b , graduations = g and weddings = w

1 ) b+g+w = 40

and 

2) w = b+g

Substituting 2 in 1, we get

b+g+ (b+g) = 40

Hence b+g = 20

and b = 20-g


Again substituting in equation 2

w = 20-g+g

Hence w = 20


Coming to the revenue function, 

3250 = 100w + 75b + 50 g

Dividing by 25

130 = 4w+ 3b + 2g

We know that w = 20 and b=20-g

130 = 4*20 + 3 (20-g) + 2g

130 = 80 + 60 - 3g +2g

130 = 140 -g

g = 10


Hence b = 20 - 10 = 10

Number of weddings = 20 , birthday parties = 10 and graduations = 10

Please let me know if you need any clarification. I'm always happy to answer your questions.
Dec 1st, 2015

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