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CFL Bulbs. The graph below shows how a more expensive, but more energy-efficient, compact fluorescent light bulb eventually costs less to use than an incandescent light bulb. The equation $60 c-d=96$ approximates the cost $c$ (in dollars) to purchase and use a CFL. bulb 8 hours a day for $d$ days. The equation $15 c-d=6$ does the same for an incandescent bulb. Use the elimination method to determine after how many days the upgrade to a CFL bulb begins to save money.
GRAPH CANNOT COPY.
After 24 days
Algebra
Chapter 4
Systems of Linear Equations and Inequalities
Section 3
Solving Systems of Equations by Elimination (Addition)
Equations and Inequalities
Systems of Equations and Inequalities
Oregon State University
Harvey Mudd College
Baylor University
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These are the two equations from the problem where d equals the number of days of using the light bulb, and C equals the cost. And what we're looking for is how many days it will take for the Ah CFL Bowl to surpass the incandescent in terms of savings. So when will the CFL bulb actually cost us less? And so to do that, we want to find the intersection point and to find the intersection point for this system, it would make sense to multiply one of the equations by negative one and then used the elimination method. So I'm going to leave the first equation as it is and multiply the second equation by negative one. That way we have opposite de terms, and we can add the equations together, and the D terms will be eliminated. And what we'll have left is 45. C equals 90. Divide both sides by 45 we get C equals two. Now that tells us the cost, and we want to know the number of days. So let's keep going and find the value of D. So I'm going to take that number and substituted into one of my equations might as well substituted into the top one. 60 times two minus D equals 96. So 1 20 minus D equals 96 we can subtract 1 20 from both sides and get negative 24. So then, when we multiply both sides of the equation by a negative one, we get D equals 24 that tells us that they cost the same amount at day 24. So after day 24 the CFL bulb will cost less.
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