Question

A store sells televisions for $360 and DVD burners for $270. The entire stock is worth $52,920 and there are a total of 164 televisions and DVD burners combined. How many of each on are there?

Answer 1

Let's call the number of televisions "t" and the number of DVD burners "d".

From the problem, we know that:

- The cost of one television is $360, so the value of t televisions is 360t.
- The cost of one DVD burner is $270, so the value of d DVD burners is 270d.
- The entire stock is worth $52,920, so we can write an equation:

360t + 270d = 52,920

We also know that there are a total of 164 televisions and DVD burners combined, so we can write another equation:

t + d = 164

Now we have two equations with two variables, and we can solve for t and d.

Let's solve the second equation for t:

t + d = 164

t = 164 - d

Now we can substitute this expression for t into the first equation:

360t + 270d = 52,920

360(164 - d) + 270d = 52,920

59,040 - 360d + 270d = 52,920

-90d = -6,120

d = 68

So there are 68 DVD burners. We can use the equation we found for t to find the number of televisions:

t = 164 - d

t = 164 - 68

t = 96

So there are 96 televisions.

Check:

- The value of 68 DVD burners at $270 each is 68 x 270 = $18,360.
- The value of 96 televisions at $360 each is 96 x 360 = $34,560.
- The total value is $18,360 + $34,560 = $52,920, as expected.