need help with these 3 problems PLEASE!!!?

Question

1) The larger of 2 complementary angles measures 6 degrees less than twice the smaller angle. Find the degree measure of each angle.

2) 3 pretzels and 1 cup of soda cost $2.75. 2 pretzels and 1 soda cost $2.00. Find the cost of a pretzel and the cost of a soda.

3) A baseball manager bought 4 bats and 9 balls for $76.50. On another day, she bought 3 bats and 12 balls at the same prices and paid $81.00. How much did she pay for each bat and each ball?

Answer 1

More angles! Cool!
(1) Complementary angles add up to 90 degrees
Lets call them x and 90-x

Larger one is 6 degrees less than twice the smaller

So ... 90-x + 6 = 2x

ie 96 = 3x

The two angles are
x = 32 degrees
90-x = 58 degrees

(2) If 2 pretzels and a soda cost $2.00 and 3 pretzels and 1 soda cost $2.75

Then 1 pretzel costs $0.75

Therefore, 1 pretzel and 1 soda = $1.25

(3) 4 bats and 9 balls cost $76.50
3 bats and 12 balls cost $81.00

Let the bats cost x and the balls cost y

4x + 9y = 76.50 {equation 1}
3x + 12y = 81.00 {equation 2}

12y = 81.00 - 3x
y = (81-3x)/12

4x + 9(81-3x)/12 = 76.50

4x + 3(81-3x)/4 = 76.50
16x + 3(81-3x) = 4(76.50)
16x + 243 - 9x = 306

7x = 306 - 243
x = 63/7
x = 9

The bats cost $9.00 ea

y = (81-3x)/12
= (81-27)/12
= 9/2

The balls cost $4.50 ea

Answer 2

Here's a hint for problem 2. Let P be the cost of a pretzel and S be the cost of a soda.
Then
3P + S = 2.75
2P + S = 2.00

Subtract the second equation from the first to get the price of P. When you know P, you can find S easily. Use the same technique for the third problem.

Answer 3

1) 2x-6+x=90
3x-6=90
3x=96
x=32
small angle is 32 degrees, large is 58

2) each pretzel is $0.75. the soda is $0.50

3)3 balls equals 1 bat + $4.50
4 bats + 3bats + 13.50=$76.50
7 bats=$63.00
1 bat is $9.00
one ball is $4.50

I did not show the work. You can figure that out.

Answer 4

angles x + y + z = 180
complementary larger angle x = 90 - z, smallest angle z

90-z -6 = 2 z
90 - 6 = 3z
z = 84/3= 28
x = 90 - 28 = 62
y = 180 - 28 - 62 = 90

2) 3p + 1s = 2.75----(1)
2p + 1 s = 2-------(2)
(1)-(2)=> p = 0.75 and s = 2-1.5=0.5

3) 4x + 9y = 76.5
3x + 12 y = 81 => x = (81 - 12y)/3

4(81 -12y)/3 + 9y = 76.5
108 - 16y + 9y = 76.5
7y = 31.5
y=4.5
x= 9

Answer 5

1)
(2A-6) + A = 90
3A=96
A=32
B=58


2)

a) 3P + 1S = 275
b) 2P + 1S = 200 x-1

c) -2P - 1S = -200

Adding a and c gives

P=0.75$ Pretzel Price

Substitute in b

150 + S = 275
S = 1.25 Soda Price


3)


Bats = A and Ball = B


4A + 9B = 7650 x-3
3A + 12B = 8100 x4


-12A -27B = -22950
12A + 48B = 32400
__________________+

21B = 9450
B = 4.50$ Price of each ball
A= 9.00$ Price of each bat