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?
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.
Let's denote the number of televisions as "t" and the number of DVD burners as "d".
We are given two pieces of information:
1) The price of one television is $360, so the value of "t" televisions can be expressed as 360t.
2) The price of one DVD burner is $270, so the value of "d" DVD burners can be expressed as 270d.
We know that the total value of the stock is $52,920, so we can set up the equation:
360t + 270d = 52,920 (equation 1)
We also know that the total number of televisions and DVD burners combined is 164, so we can set up another equation:
t + d = 164 (equation 2)
Now we have a system of two equations with two variables. We can use substitution or elimination to solve for "t" and "d". Let's use elimination:
Multiplying equation 2 by 270, we get:
270t + 270d = 44,280 (equation 3)
Now we can subtract equation 3 from equation 1 to eliminate the variable "d":
(360t + 270d) - (270t + 270d) = 52,920 - 44,280
90t = 8,640
Dividing both sides by 90, we find:
t = 96
Now we can substitute the value of "t" into equation 2 to find "d":
96 + d = 164
d = 164 - 96
d = 68
Therefore, there are 96 televisions and 68 DVD burners.
To solve this problem, we can set up a system of equations based on the given information.
Let's use the variables T for televisions and D for DVD burners.
From the given information, we can write the following equations:
1) The total value of televisions is $360 multiplied by the number of televisions (T): 360T.
2) The total value of DVD burners is $270 multiplied by the number of DVD burners (D): 270D.
3) The total value of all the items combined is $52,920: 360T + 270D = 52,920.
4) The total number of items is 164: T + D = 164.
Now, we can use these two equations to solve for T and D.
We can rearrange equation 4 to express T in terms of D: T = 164 - D.
Next, substitute this value for T in equation 3: 360(164 - D) + 270D = 52,920.
Expanding this equation gives: 59,040 - 360D + 270D = 52,920.
Combining like terms, we get: -90D = -6,120.
Dividing both sides by -90 gives: D = 68.
Now substitute the value of D back into equation 4 to find T: T = 164 - 68 = 96.
Therefore, there are 96 televisions and 68 DVD burners in the store.