6) A wallpaper store determines that the daily revenue (in
pesos) earned by the store on the sale of y square meters of
wallpaper is given by the equation R = y²-65y. How many
square meters of wallpaper must be sold if the revenue from
the wallpaper is to be php 1200 per day?
Answer:
the store must sell 80 square meters of wallpaper to reach a revenue of Php 1200 per day.
Solution:
To find out how many square meters of wallpaper must be sold to reach a revenue of Php 1200 per day, we need to set the equation R = 1200 and solve for y.
The given equation is: R = y² – 65y
Substituting R with 1200, we have: 1200 = y² – 65y
Rearranging the equation to make it quadratic, we have: y² – 65y – 1200 = 0
To solve this quadratic equation, we can either factor it or use the quadratic formula. Let’s use the quadratic formula:
y = (-b ± sqrt(b² – 4ac)) / (2a)
For this equation, a = 1, b = -65, and c = -1200.
Plugging these values into the quadratic formula, we have:
y = (-(-65) ± sqrt((-65)² – 4(1)(-1200))) / (2(1))
Simplifying further:
y = (65 ± sqrt(4225 + 4800)) / 2
y = (65 ± sqrt(9025)) / 2
y = (65 ± 95) / 2
Now we have two possible solutions:
y₁ = (65 + 95) / 2 = 160 / 2 = 80
y₂ = (65 – 95) / 2 = -30 / 2 = -15
Since we are dealing with the number of square meters of wallpaper, a negative value like -15 does not make sense in this context. Therefore, we take the positive solution.
So, the store must sell 80 square meters of wallpaper to reach a revenue of Php 1200 per day.
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