SOLUTION: The St. Mark�s Community Barbecue served 250 dinners. A child�s plate cost $3.50 and an adult�s plate cost $7.00. A total of $1347.50 was collected. How many of each type of plate

Question 201973: The St. Mark�s Community Barbecue served 250 dinners. A child�s plate cost $3.50 and an adult�s plate cost $7.00. A total of $1347.50 was collected. How many of each type of plate was served?

Thank you!!!
Answer by PRMath(133) (Show Source): You can put this solution on YOUR website!
I answered this question already. Maybe you did not find the answer, so I will copy and paste my original answer here. I hope you find it this time......
Let's just get this to the facts:

A child's plate: 3.50 (Let's refer to this as "C" for child)
Adult's plate: 7.00 (Let's refer to this as "A" for adult)
Total dinners served: 250
Total amount collected: 1,347.50

So, there are two equations to think about here:
C + A = 250 dinners. (Child plates and adult plates = 250)
3.5C + 7.0A = 1,347.5 (Child cost TIMES the number of plates and Adult cost TIMES the number of plates will total 1,347.5)

Ok, at your first equation: C + A = 250, let's just rewrite that and solve for "C"

C + A = 250
C = 250 - A (subtract "A" from both sides)

Now let's look at your 2nd equation: 3.5C + 7.0A = 1,347.5
How about "plugging" in the value of C that we found above? If C = 250 - A, then let's put 250 - A in place of the "C" that is in the above equation.

SO, we have:
3.5C + 7.0A = 1,347.5
3.5(250 - A) + 7.0A = 1,347.5
875 - 3.5A + 7.0A = 1,347.5 (I just distributed 3.5 times 250 and 3.5 times -A)
875 + 3.5A = 1,347.5 (I just combined the "A" terms: -3.5A + 7.0A = +3.5A)
3.5A = 472.5 (I subtracted 875 from both sides)
A = 135 (I divided both sides by 3.5)

So there were 135 adult plates. How many children plates were there? Well there were 250 plates TOTAL, sooooo,

250 total plates MINUS 135 adult plates = 115 Child plates.

Therefore, our final answer is 135 Adult plates and 115 child plates.

Let's check to see if we are right...........
135 Adult plates tiimes $7.0 = $945.00
115 Child plates times $3.50 = 402.50
________________________________________
250 Total plates $1,347.50 total amount of money raised.

We are correct. yay. :-)
Hope this helped. :-)

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