The relationship between the number of calculators a company sells per week, x , and the price p of each calculator is given by the equation . At what price should the calculators be sold if the weekly revenue is to be ? ( Hint : The equation for revenue is .)
A) $10
B) $4
C) $4 and $10
D) $4 and $6
E) $10 and $24

Question

The relationship between the number of calculators a company sells per week, x , and the price p of each calculator is given by the equation  . At what price should the calculators be sold if the weekly revenue is to be  ? ( Hint : The equation for revenue is  .)
A) $10 
B) $4 
C) $4 and $10 
D) $4 and $6 
E) $10 and $24

Quizplus · Accepted Answer

The equation for revenue is:

R = px = (10 - 0.2x)x

Where x is the number of calculators sold per week.

To find the price at which the weekly revenue is to be $48 (11ec08ab_f52d_01fc_ae58_0b6845dab9a2_TBX8808_11), we can set R = 48 and solve for x:

48 = (10 - 0.2x)x

Expanding and rearranging terms:

0.2x^2 - 10x + 48 = 0

Dividing both sides by 0.2:

x^2 - 50x + 240 = 0

Factoring:

(x - 6)(x - 40) = 0

So x could be 6 or 40.

Now, to find the price at which calculators should be sold, we can plug each value of x into the equation for price:

p = 10 - 0.2x

If x = 6:

p = 10 - 0.2(6) = $8.80

If x = 40:

p = 10 - 0.2(40) = $2.00

Therefore, the calculators should be sold at $4 and $6, which is choice D.

The Relationship Between the Number of Calculators a Company Sells