Answer:
(3,2)
Step-by-step explanation:
The system is
x + y = 5
x -y = 1
Add the equations to eliminate y
2x = 6----->x=3
Substitute this value in any equation
3+y = 5----->y=2
The solution is (3,2)
Answer: 199.5
Step-by-step explanation: 9.5 x 10.5 hours x 2 weeks
Answers:
- Total equation: x+y = 80
- Legs equation: 2x+4y = 248
- How many ducks? 36
- How many cows? 44
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Further explanation:
- x = number of ducks
- y = number of cows
x+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.
That equation can be solved to y = 80-x after subtracting x from both sides.
The legs equation is 2x+4y = 248 because...
- 2x = number of legs from all the ducks only
- 4y = number of legs from all the cows only
- 2x+4y = total number of legs from both types of animals combined
We're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248
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Let's plug y = 80-x into the second equation and solve for x.
2x+4y = 248
2x+4( y ) = 248
2x+4( 80-x ) = 248
2x+320-4x = 248
-2x+320 = 248
-2x = 248-320
-2x = -72
x = -72/(-2)
x = 36
There are 36 ducks
Now use this x value to find y
y = 80-x
y = 80-36
y = 44
There are 44 cows.
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Check:
36 ducks + 44 cows = 80 animals total
36*2 + 44*4 = 72 + 176 = 248 legs total
The answers are confirmed.
hope it will help you..........
Answer:
The price of an adult ticket it $5
Step-by-step explanation:
To solve this, we would find the system of equations. We would set up two equations that will represent the situation.
Let c = price per children ticket
Let a = price per adult ticket
Santo:
5c + 1a = 16.25
Hulda:
4c + 3a = 24
5c + 1a = 16.25 -> a = 16.25 - 5c
4c + 3a = 24
4c + 3(16.25 - 5c) = 24
4c + 48.75 - 15c = 24
-11c + 48.75 = 24
-48.75 -48.75
-11c = -24.75
/-11 /-11
c = 2.25
5c + a = 16.25
5(2.25) + a = 16.25
11.25 + a = 16.25
-11.25 -11.25
a = 5
a = $5 , c = $2.25
