Question

extra credit:
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 (\begin{cases}d = 923-12t\\d = 505 + 26tend{cases}) 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 (square) dvds and blu - ray discs sold per month in (square) months.

Explanation:

Step1: Set equations equal to each other

Since both expressions equal $d$, substitute:
$923 - 12t = 505 + 26t$

Step2: Isolate $t$ terms

Add $12t$ to both sides:
$923 = 505 + 38t$

Step3: Isolate constant terms

Subtract 505 from both sides:
$923 - 505 = 38t$
$418 = 38t$

Step4: Solve for $t$

Divide both sides by 38:
$t = \frac{418}{38} = 11$

Step5: Solve for $d$

Substitute $t=11$ into $d=923-12t$:
$d = 923 - 12(11) = 923 - 132 = 791$

Answer:

There will be 791 DVDs and Blu-Ray discs sold per month in 11 months.