6) A Wallpaper Store Determines That The Daily Revenue (in P…

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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