A bicycle store costs $3600 per month to operate. The store pays an average of $35 per bike. The average selling price of each bicycle is $155. How many bicycles must the store sell each month to break even?
(Type a whole number.)
Let's assume the number of bicycles sold in a month is x.
The total cost for the store to operate in a month is $3600.
The cost of each bike sold is $35.
So, the total cost of bikes sold in a month is 35x.
The selling price of each bike is $155.
So, the total revenue from selling bikes in a month is 155x.
For the store to break even, the total revenue must be equal to the total cost:
155x = 3600 + 35x
Simplifying the equation:
120x = 3600
x = 3600 / 120
x = 30
Therefore, the store must sell 30 bicycles each month to break even.
A metalworker has a metal alloy that is 30% copper and another alloy that is 60% copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 48% copper alloy.
Let's assume x kilograms of the 30% copper alloy will be combined and (100 - x) kilograms of the 60% copper alloy will be combined to make 100 kg of a 48% copper alloy.
The amount of copper in the 30% copper alloy is 0.30x kg.
The amount of copper in the 60% copper alloy is 0.60(100 - x) kg.
In the 48% copper alloy, the amount of copper is 0.48 * 100 kg.
Setting up the equation for the total amount of copper in the final alloy:
0.30x + 0.60(100 - x) = 0.48 * 100
Simplifying the equation:
0.30x + 60 - 0.60x = 48
Combining like terms:
0.30x - 0.60x = 48 - 60
-0.30x = -12
Dividing both sides by -0.30:
x = -12 / -0.30
x = 40
Therefore, the metalworker should combine 40 kilograms of the 30% copper alloy and (100 - 40) = 60 kilograms of the 60% copper alloy to create 100 kg of a 48% copper alloy.
Gabe Amodeo, a nuclear physicist, needs 60 liters of a 40% acid solution. He currently has a 20% solution and a 50% solution. How many liters of each does he need to make the needed 60 liters of 40% acid solution?
Let's assume Gabe needs x liters of the 20% acid solution and (60 - x) liters of the 50% acid solution to make 60 liters of a 40% acid solution.
The amount of acid in the 20% solution is 0.20x liters.
The amount of acid in the 50% solution is 0.50(60 - x) liters.
In the 40% acid solution, the amount of acid is 0.40 * 60 liters.
Setting up the equation for the total amount of acid in the final solution:
0.20x + 0.50(60 - x) = 0.40 * 60
Simplifying the equation:
0.20x + 30 - 0.50x = 24
Combining like terms:
0.20x - 0.50x = 24 - 30
-0.30x = -6
Dividing both sides by -0.30:
x = -6 / -0.30
x = 20
Therefore, Gabe needs 20 liters of the 20% acid solution and (60 - 20) = 40 liters of the 50% acid solution to make 60 liters of a 40% acid solution.
Determine whether the ordered pair is a solution of the given inequality.
y ≤ - 4x + 1; (1,0)
Is (1,0) a solution of the given inequality?
Yes
No
To determine if the ordered pair (1,0) is a solution of the inequality y ≤ -4x + 1, we substitute the values of x and y into the inequality:
0 ≤ -4(1) + 1
Simplifying the equation:
0 ≤ -4 + 1
0 ≤ -3
Since 0 is less than -3, the statement is false. Therefore, the ordered pair (1,0) is not a solution of the given inequality.
No.