What is the solution to the system? use elimination .
-18.6x+ 17.2y=90.2
14.2x+ 3.4y= -35.8
a.(3,2)
b.(-3,2)
c.(2/3,4/9)
d.(2,3)
IS IT D??
Terry and ed start a lawn mowing business and purchase mowers and equipment for $800. They charge $20 for each lawn and $4 worth of gas for each job. How many laws must Terry and Ed mow before breaking even?
a .34 lawns
b. 40 lawns
c. 50 lawns
d. 20 lawns
IS IT A ????
At the local ballpark, the team charges $5.00 for each ticket and expects to make $1,300.00 in concessions. the team must pay in players $1,800.00 and pay all the workers $1,500.00. Each fan gets a free bat, costs the team $3.00 per bat of the following, what is the smallest number of tickets that must be sold to break even???
a. 2,300 tickets
b. 400 tickets
c .250 tickets
d. 1,000 tickets
IS IT D????
Someone help!!!
To solve the system of equations using elimination, we need to eliminate one variable by multiplying one or both equations by a constant so that when we add or subtract the equations, one variable cancels out. Here's how to do it:
-18.6x + 17.2y = 90.2 (Equation 1)
14.2x + 3.4y = -35.8 (Equation 2)
Let's multiply Equation 2 by -5.1 (this will make the x coefficients equal):
-5.1(14.2x + 3.4y) = -5.1(-35.8)
-72.42x - 17.34y = 182.58 (Equation 3)
Now, add Equation 1 and Equation 3:
(-18.6x + 17.2y) + (-72.42x - 17.34y) = 90.2 + 182.58
-90.02x - 0.14y = 272.78
Simplify:
-90.02x = 272.78
x = 272.78 / -90.02
x ≈ -3.03
Substitute the value of x into Equation 1:
-18.6(-3.03) + 17.2y = 90.2
55.24 + 17.2y = 90.2
17.2y = 34.96
y = 34.96 / 17.2
y ≈ 2.03
So the solution to the system of equations is approximately (x = -3.03, y = 2.03). Therefore, the correct answer is b. (-3,2).
Now let's move on to the second question:
To find out how many lawns Terry and Ed must mow before breaking even, we need to consider the costs and revenues involved.
The initial cost of mowers and equipment is $800.
For each lawn mowed, Terry and Ed earn $20, but they also spend $4 on gas. This means they earn a net profit of $20 - $4 = $16 per lawn.
To break even, Terry and Ed need to cover the initial cost of $800. So the number of lawns they must mow is:
Number of lawns = Initial cost / Net profit per lawn
Number of lawns = $800 / $16
Number of lawns = 50
Therefore, the correct answer is c. 50 lawns.
Finally, let's solve the third question:
The team charges $5 for each ticket, and they expect to make $1,300 in concessions. However, they have expenses to cover. They must pay players $1,800 and workers $1,500. Additionally, each fan receives a free bat that costs $3 per bat.
Let's set up the equation to find the minimum number of tickets they must sell to break even:
Total revenue = Total expenses
Total revenue = (Ticket price × Number of tickets) + Concession income
Total expenses = Player salaries + Worker salaries + (Number of tickets × Bat cost)
$5(Number of tickets) + $1,300 = $1,800 + $1,500 + ($3 × Number of tickets)
Simplifying the equation:
$5(Number of tickets) + $1,300 = $3(Number of tickets) + $3,300
Subtracting $3(Number of tickets) from both sides:
$2(Number of tickets) + $1,300 = $3,300
Subtracting $1,300 from both sides:
$2(Number of tickets) = $3,300 - $1,300
$2(Number of tickets) = $2,000
Dividing both sides by $2:
(Number of tickets) = $2,000 / $2
(Number of tickets) = 1,000
Therefore, the correct answer is d. 1,000 tickets.