Radha owns a Mobile showroom of a popular brand. The number of mobiles sold by the shop can be modelled by the expression N(t) = 7t+25 and the Selling price per mobile is modelled by an expression S(t)= 2t2 + 25t + 12 , where t is the number of months in a year. (I) Find the number of mobiles sold in one and half years. (ii) Choose the expression which show the amount of revenue generated by the showroom a) (2t + 1) (t-12) (7t +25) b) ( 2t + 1) (t+12) (7t +25) c) (7t+25) (2t-1) (t+12) d )none of these (iii) What is the total amount of revenue generated by the showroom at the end of the year ?
Answers
Answer:
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The answers are,
(i)The number of mobiles sold in one and half years = 151
(ii)The correct answer is option (b) (7t+25)(t + 12)(2t + 1)
(iii)The total amount of revenue generated by the showroom at end of years = 65400
Given:
The number of mobiles sold by the shop can be modelled by the expression N(t) = 7t+25
Selling price per mobile is modelled by an expression S(t)= 2t² + 25t + 12
Where t is number of months
To find:
(I) Find the number of mobiles sold in one and half years.
(ii) Choose the expression which show the amount of revenue generated by the showroom
(iii) What is the total amount of revenue generated by the showroom at the end of the year ?
Solution:
Given Number of mobiles sold N(t) = 7t+25
Selling price S(t)= 2t² + 25t + 12
(I) Find the number of mobiles sold in one and half years.
Here, given time period = one and half years
As we know 1 year = 12 months
⇒ one and half years = 12 + 6 = 18 months
Given number of mobiles sold in t months N(t) = 7t+25
The Number of mobiles sold in 18 months,
N(18) = 7(18) + 25 = 126 + 25 = 151
The number of mobiles sold in one and half years = 151
(ii) Choose the expression which show the amount of revenue generated by the showroom
Given number of mobiles sold, N(t) = 7t+25
Selling price S(t)= 2t² + 25t + 12
The amount of revenue generated by the showroom
= Number of mobiles × Selling price = N(t) × S(t)
= (7t+25)(2t² + 25t + 12)
Amount of revenue generated by the showroom=(7t+25)(2t² + 25t + 12)
Factorize (2t² + 25t + 12)
⇒ 2t² + 24t + t + 12 [ split 25t = 24t + t ]
⇒ 2t (t + 12) + (t + 12)
⇒ (t + 12) (2t + 1)
Amount of revenue generated by the showroom = (7t+25)(t + 12)(2t + 1)
The correct answer is option (b) (7t+25)(t + 12)(2t + 1)
(iii) What is the total amount of revenue generated by the showroom at the end of the year ?
Here given time period = 1 year = 12 months
The total amount of revenue generated by the showroom = (7t+25)(t + 12)(2t + 1)
Take t = 12 months
=> (7(12) + 25) (12+12)(2(12) + 1)
= (84 + 25)(24)(25)
= (109)(600)
= 65400
The total amount of revenue generated by the showroom at end of years = 65400
The answers are,
(i)The number of mobiles sold in one and half years = 151
(ii)The correct answer is option (b) (7t+25)(t + 12)(2t + 1)
(iii)The total amount of revenue generated by the showroom at end of years = 65400
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