In one day, a store sold 4/5 as many DVD's as Blu-Ray's discs. The total number of DVD's and Blu-Ray's discs sold that day was 504. How many DVD's were sold?

Question

Could you please specify every step so I make sure to understand it? Thank you.

Answer 1

Store sells 4/5 as many DVDs as Blue Rays

So using that we can set up an equation: (4/5)*D = B

where D = DVDs sold and B is the amount of Blue Rays sold.

The total number of DVD's and Blue Rays sold were 504.

So there were 504 total sold of both types.

From here we can set up another equation.

D + B = 504

Where D is equal to the DVD's sold while B is equal to the blue rays sold.

previously, we were told that 4/5s as many DVDs were sold compared to blue ray, so this is where the first equation comes into the problem.

Since (4/5)*D = B we can substitute this into the D+B=504 equation

so it will now be:

D + (4/5)*D = 504

which simplifies to

(9/5)*D = 504

From here you can solve for D (multiply 5 on both sides)

9*D = 2520

and then divide by 9 on both sides to get D (DVDs sold)

D = 280

We see that the amount of DVDs sold is 280. There are two ways to solve for the Blue rays sold.

One way is subsitute D into the (4/5)*D = B equation

where (4/5)*D = B ----> (4/5)*(280) = B which is 224.

The other way is to substitute D into the D+B = 504 equation

where 280 + B = 504 ---> subtract 280 on both sides

to get B = 504 - 280 = 224

so

amount of DVD's sold is 280

amount of Blue Rays sold is 224