Question 1192915: An electronics company makes two types of switches. Type A takes 3 minutes to make and requires $2 worth of materials. Type B takes 6 minutes to make and requires $6 of materials. In the latest production batch, it took 36 hours to make these switches, and the materials cost $1960. How many of each type of switch were made?
There were ___ Type A switches and ____ Type B switches manufactured.
Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
x = number of type A switches made
y = number of type B switches made
x and y are nonnegative integers
A single type A switch takes 3 minutes to make, so it takes 3x minutes to make all x type A switches.
Eg: if you had x = 5 type A switches, then it takes 3x = 3*5 = 15 minutes to make all five of them.
A type B switch takes 6 minutes to make, so making y of them will take up 6y minutes.
In total, it takes 3x+6y minutes to make both types of switches. It takes 36 hours, aka 36*60 = 2160 minutes, to make all the switches mentioned.
Therefore, we end up with this equation
3x+6y = 2160
Divide everything by 3 to get
x+2y = 720
Then isolate x to get
x = -2y+720
Now to form the other equation.
Type A costs $2 per switch, so making x switches costs 2x dollars.
Similarly, type B costs $6 per switch to cost 6y dollars.
The total cost is 2x+6y, which is set equal to $1960
2x+6y = 1960
2(x+3y) = 1960
x+3y = 1960/2
x+3y = 980
Let's plug in x = -2y+720 and solve for y
x+3y = 980
-2y+720+3y = 980
y+720 = 980
y = 980-720
y = 260
This is the number of type B switches made.
This leads to,
x = -2y+720
x = -2(260)+720
x = -520+720
x = 200
This is the number of type A switches.
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Answer:
Number of type A switches = 200
Number of type B switches = 260
Answer by greenestamps(13200)  (Show Source):
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