Question 1:- A streaming video service offers its customers two plans. The first plan has a $ 24 registration fee, a fixed monthly rate of $5 and a charge of $0.75 for each video download. The second plan has a $15 registration fee, a fixed monthly rate of $3 and a charge of $1.50 for each vedio download. For how many download would the two plans cost the same for a year of service ?
Solution:- Let the number of download = x video
First plan
Registration fee = $24
a charge for each video download = $0.75
Monthly rate for the fixed charge of first plan = $5 × 12 = $60
Total cost for the first plan = 24 +60 + 0.75 x = 84 + 0.75 x
Second plan
Registration fee = $15
a charge for each video download = $1.50
Monthly rate for the fixed charge of first plan = $3 × 12 = $36
Total cost for the first plan = 15 +36 + 1.50 x = 51 + 1.50 x
Now, the two plans cost the same for a year of service
84 + 0.75 x = 51 + 1.50 x
⇒ 84 – 51 = 1.50 x – 0.75 x
⇒ 33 = 0.75 x
⇒ 33 = 3/4 x
⇒ 
⇒ x = 44
Thus, the number of download = 44
Question 2:- The length of a rectangle is three times its width. A new rectangle is created by decreasing the length of the original rectangle by 9 feet and increasing its width by 4 feet. The area of the new rectangle is the same as the area of the original rectangle. What is the perimeter of the new rectanle ?
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