5 question :D = 10 points!?

The Carmike 14 Theatre charges $8 for an adult ticket and $4.50 for a child鈥檚 ticket. On a particular Friday night, the entire 950 seat theater was full. The total ticket receipts for the evening were $6462.50. How many of each type of ticket were sold?





Jeff Reed is the kicker for the Pittsburgh Steelers and is currently their top scorer. As a kicker, he can score two ways. A field goal is worth 3 points and the extra point after a touchdown is worth 1 point. Jeff has scored 37 points with 19 kicks. How many of his kicks were field goals, and how many were extra points?





The International Club sold 300 lb of granola bars and collected $111. The peanut butter bars cost 40垄 per lb, and the chocolate chip costs 35垄 per lb. How many pounds of each type were sold?



A landscaper planted some trees and bushes on a property. His first order was for 13 bushes and 4 trees and cost $487. The second order was for 6 bushes and 2 trees and cost $232. Find the price of each tree and bush.



Your family went to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80 and some order the steak dinner for $17. If the total bill was $91, how many people ordered each type of dinner?5 question :D = 10 points!?
OK I'm doing the 1st 2, you do the rest. It's the same approach.



A= adult tickets sold

C = child tickets sold



$8/adult x A + $4.50/child x C = $6,462.50

(1) 8A + 4.5C = 6462.50



(2) A + C = 950 %26lt;-- number of tickets sold = 950



solve for A and C (2 equations, 2 unknowns)



From (2) C = 950 - A

Substitute into (1)

8A + 4.5(950 - A) = 6462.50

8A + 4275 - 4.5A = 6462.50

8A - 4.5A = 6462.5 - 4275

3.5 A = 2187.5

A = 2187.5/3.5 = 625 adult tickets sold

C = 950 - 625 = 325 child tickets sold



2.

Note: This assumes Jeff Reed was never missed any of his kicks, either FG or PAT!



F = field goals

X =extra point kick (PAT)



(1) F + X = 19

(2) 3F + 1X = 37 %26lt;-- 3 points x no. of FG + 1 point x no. PAT



X = 19 - F

3F + (19 - F) = 37

2F = 18

F = 9 field goals made

X = 19 - 9 = 10 extra points converted!
These are simple Algebra problems, you should be doing them yourself not asking someone else to do them for you.5 question :D = 10 points!?
1 is 625 adult and 325 kids



#2 is 9 kicks and 10 extra points



There's two answers now stop being lazy and figure the rest out yourself. They are not hard they just take some time.
1. x=number of adults y=number of children x+y=950 therefore y=950-x. Now, prize:

8x + 4.5y = 6462.5,

which is the same as

8x + 4275 - 4.5x = 6462.5

3.5x = 2187.5

x=625

625 adults, 325 kids.



2. x=number of field goals y=number of extra points x+y=19 therefore y=19-x. Now, points:

3x + 1y = 37,

which is the same as

3x + 19 - x = 37,

2x = 18

x=9

9 field goals, 10 extra points.



3. x=lbs of peanut butter bars y=lbs of chocolate chips x+y=300 therefore y=300-x. Now, prize:

0.4x + 0.35y = 111,

which is the same as

0.4x + 105 - 0.35x = 111,

0.05x = 6

x=120

120 lbs of peanut butter bars, 180 lbs of chocolate chips.



4. x=number of bushes y=number of trees

6x + 2y = 232 -%26gt; y = 116 - 3x

13x + 4y = 487,

which is the same as

13x + 464 - 12x = 487

x=23

23$ bush, 47$ tree



5. x=number of people having chicken y=number of those having steaks x+y=6 therefore y=6-x. Now, money paid:

14,8x + 17y = 91,

which is the same as

14.8x + 102 - 17x = 91

-2,2x = 11

x=5

5 of them had chicken, 1 had steak