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Question

1a.At the high school band's annual spaghetti dinner, the members served 210 dinners and collected $935. The band leader did not designate which ticket was an adult or child dinner. You need to know that to prepare the correct amount of food and for future planning. Each adult dinner cost $6 and each child's dinner cost $3.50.

Let a = number of adult dinners

Let c = number of child dinners

1b. Write two equations to represent the total amount raised from the dinner and the total

2. Use substitution to solve the above system of equations. How many adult dinners were sold and how many child dinners were sold?

pleas Show all work

3. Pleas Show all work to receive full credit for this problem.

Use the Substitution method to solve the system of equations. Give your answer as an ordered pair (x,y).

x y = -5

x - y = 3

4. Choose the ordered pair that is a solution to the system of equations.

3x y = 5

4x - 7y = -10

(-1,2)

(1,2)

(-1,-2)

(1, -2)

5. Choose the ordered pair that is a solution to the system of equations.

y - x = 5

2y x=-2

(-4,-1)

(-1,-4)

(-4, 1)

(4, -1)

6. The sum of two numbers is 28. The larger number, y, is 4 more than the smaller number, x. Write two equations for this system and solve to find x and y.

Give your answer as an ordered pair without parentheses or spaces, as in x,y.

Answer 1

1b)  a + c = 210 (the equation for how many people ate)

     6a + 3.5c = 935 (the equation for the cost for the people)

2)  

     a = 210 - c  according to the first equation

So, substitute:

6(210 - c) + 3.5c = 935

1260 - 6c + 3.5c = 935

solve for c....  then plug that c into one of the original equations from (1b) and solve for a.

3)

x + y = -5

x - y = 3

So, change the second equation to:

x = 3 + y

Substitute into first equation

(3+y)+ y = -5

2y + 3 = -5

2y = -8

y = -4

x = 3+y

x = 3 + (-4)

x = -1

4)  

3x + y = 5

4x - 7y = -10

So, y = 5 -3x

4x - 7(5 - 3x) = -10

4x - 35 + 21x = -10

25x = 25

x = 1

3(1) + y = 5

y = 2

So,

(1,2)

5)

y - x = 5

2y + x=-2

multiply the first equation by 2:

2y - 2x = 10

2y + x = -2  (subtracting second equation from first-- linear combination)

___________

-3x = 12

x = -4

2y + (-4) = -2

2y = 2

y = 1

(-4, 1)

6)

x + y = 28

y = 4+ x

Plug the second equation into first

x + (4 + x) = 28

4 + 2x = 28

2x = 24

x = 12

12 + y = 28

y = 16

(12, 16)