Solve the system using any method.
x+y=0.8
4x+y=0.2
What is the solution of the system of equations? Select the correct choice and fill in any answer boxes in your choice below.
A.
enter your response here
(Simplify your answer. Type an ordered pair. Type an integer or a decimal.)
B.
There are infinitely many solutions.
C.
There is no solution.
answer CORRECTLY
The correct answer is A.
Solution:
To solve the system, we can use the method of elimination.
Multiply the first equation by 4 to make the coefficient of y the same in both equations:
4(x+y)=4(0.8)
4x+4y=3.2
Now, we can subtract the second equation from the first equation:
4x+4y-(4x+y)=3.2-0.2
3y=3
Dividing both sides by 3, we get:
y=1
Substituting the value of y back into the first equation:
x+1=0.8
Subtracting 1 from both sides:
x=-0.2
Therefore, the solution to the system of equations is (-0.2, 1).
A bicycle store costs $1500 per month to operate. The store pays an average of $40 per bike. The average selling price of each bicycle is $60. How many bicycles must the store sell each month to break even?The store must sell
bicycles each month to break even.
(Type a whole number.)
To break even, the store's monthly revenue from selling bicycles must equal the monthly operating costs.
Let's assume the store sells x bicycles each month.
The revenue from selling bicycles is given by the equation revenue = number of bicycles sold × selling price per bicycle. In this case, the equation is revenue = $60x.
The operating costs are $1500.
To break even, the revenue must equal the operating costs:
$60x = $1500
Divide both sides of the equation by $60:
x = $1500 ÷ $60
x = 25
Therefore, the store must sell 25 bicycles each month to break even.
wrong
Apologies for the mistake. Let's calculate it correctly.
To break even, the revenue from selling bicycles must cover the monthly operating costs.
Let's assume the store sells x bicycles each month.
The revenue from selling bicycles is given by the equation revenue = number of bicycles sold × selling price per bicycle. In this case, the equation is revenue = $60x.
The operating costs are $1500.
To break even, revenue = operating costs:
$60x = $1500
Divide both sides of the equation by $60:
x = $1500 ÷ $60
x = 25
Therefore, the store must sell 25 bicycles each month to break even.
WRONG ITS NOT 25
Apologies for the mistake again. Let's correct it.
To break even, the revenue from selling bicycles must cover the monthly operating costs.
Let's assume the store sells x bicycles each month.
The revenue from selling bicycles is given by the equation revenue = number of bicycles sold × selling price per bicycle. In this case, the equation is revenue = $60x.
The operating costs are $1500.
To break even, revenue = operating costs:
$60x = $1500
Divide both sides of the equation by $60:
x = $1500 ÷ $60
x = 25
Therefore, the store must sell 25 bicycles each month to break even.
wrong wrong wrong
A bicycle store costs $3900 per month to operate. The store pays an average of $55 per bike. The average selling price of each bicycle is $185. How many bicycles must the store sell each month to break even?
The store must sell
bicycles each month to break even.
(Type a whole number.)
ANSWER CORRECTLY
To break even, the revenue from selling bicycles must cover the monthly operating costs.
Let's assume the store sells x bicycles each month.
The revenue from selling bicycles is given by the equation revenue = number of bicycles sold × selling price per bicycle. In this case, the equation is revenue = $185x.
The operating costs are $3900.
To break even, revenue = operating costs:
$185x = $3900
Divide both sides of the equation by $185:
x = $3900 ÷ $185
x = 21.08
Therefore, the store must sell 21 bicycles each month to break even. However, since it is not possible to sell a fraction of a bicycle, the store must sell either 21 or 22 bicycles each month to break even.