SOLUTION: I've been trying to work this problem, but I'm stumped. I have been trying it with the variable rate equations A=RB and variable rate + fixed rate = total rate. Here is the probl

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Question 119880: I've been trying to work this problem, but I'm stumped. I have been trying it with the variable rate equations A=RB and variable rate + fixed rate = total rate. Here is the problem: A 60watt bulb cost 50 cents to buy and 12 cents per day to use (24hrs). Another bulb cost $2.50 to buy and 2 cents per day to use. How many days of use will it take for the cost of the bulbs to be equal and what is the equivalent cost?
Found 2 solutions by stanbon, NinangS:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A 60watt bulb cost 50 cents to buy and 12 cents per day to use (24hrs). Another bulb cost $2.50 to buy and 2 cents per day to use. How many days of use will it take for the cost of the bulbs to be equal and what is the equivalent cost?
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1st Bulb Cost for x days of use: A(x) = 0.50+0.12x
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2nd Bulb Cost for x days of use: B(x) = 2.50 + 0.02x
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EQUATION:
When does A(x) = B(x) ?
0.50+0.12x = 2.50 + 0.02x
2.00 = 0.10x
x = 20 days
A and B have equivalent costs for 20 days of use.
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The cost when x=20 days:
A(20) = 0.50 + 0.12*20 = 0.50+2.40 = 2.90
B(20) = 2.50 + 0.02*20 = 2.50+40 = 2.90
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Cheers,
Stan H.

Answer by NinangS(5) (Show Source):
You can put this solution on YOUR website!
Let x represent the number of days.
The cost of the first bulb would be
0.50+0.12x
and the second would be
2.50+0.02
Since they need to be equal set up would look like this
0.50+0.12x = 2.50+0.02x
now solve for x
0.50+0.12x = 2.50+0.02x
0.12x-0.02x = 2.50-0.50
0.10x = 2.00
x = 20 days
Now to find the amount replace x with 20
0.50+0.12(20) = 2.50+0.02(20)
$2.90 = $2.90