Question

Solve the real-world situation by using the substitution method. The number of DVDs sold at a store in a month was 935 and the number of DVDs sold decreased by 12 per month. The number of Blu-ray discs sold in the same store in the same month was 517 and the number of Blu-ray discs sold increased by 26 per month. Let d represent the number of discs sold and t represent the time in months. The system of equations lbrace d = 935 − 12t d = 517 + 26t can be used to represent this situation. If this trend continues, how many months will the number of DVDs sold equal the number of Blu-ray discs sold? How many of each is sold in that month? There will be ______ DVDs and Blu-Ray discs sold per month in ______ months.

Answer 1

t = 11 months

d = 803

Explanation:

d = 935 − 12t

d = 517 + 26t

how many months will the number of DVDs sold equal the number of Blu-ray discs sold

Equate both equations to solve for the number of months

935 − 12t = 517 + 26t

935 - 517 = 26t + 12t

418 = 38t

t = 418 / 38

t = 11 months

How many of each is sold in that month?

d = 935 − 12t

= 935 - 12(11)

= 935 - 132

= 803

d = 517 + 26t

= 517 + 26(11)

= 517 + 286

d = 803

There will be 803 DVDs and Blu-Ray discs sold per month in 803 months.