Question

Solve the real-world situation by using the substitution method.

The number of DVDs sold at a store in a month was 923 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 505 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
{d=923-12t
{d=505+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

791

Explanation:

Answer 2

In 11 months, the number of DVDs sold and Blue-Ray discs sold will be same, 791 of each.

Explanation:

In the equation d = 923-12t, substitute 505+26t (from the second equation) for 'd'. We get

505 + 26t = 923 - 12t

-505 + 12t -505 + 12t

38t = 418

t=11

d = 923-12(11) = 791

d = 505+26(11) = 791

After 11 months, selling 791 of each.

Hope this helps.