juan's band produced a number of CDs to sell at a gig.the batch of CDs cost $170.00 to make and each CD was sold for $2.50 more than it cost to produce.juan gave 2 CDs to his friends,but sold the rest for a total of $198.00.How many CDs did juan produce?
20
To find out how many CDs Juan produced, we need to set up an equation based on the given information.
Let's assume that Juan produced "x" CDs.
The cost of producing each CD is given as $170.00.
So, the cost of producing "x" CDs would be $170.00 * x.
Each CD was sold for $2.50 more than it cost to produce.
Therefore, the selling price of each CD would be ($170.00 + $2.50).
Juan gave away 2 CDs to his friends, which means he sold (x - 2) CDs.
And the total amount he received from selling the remaining CDs is $198.00.
Based on this information, we can set up the equation:
($170.00 + $2.50) * (x - 2) = $198.00
Now, let's solve the equation to find the value of "x" (the number of CDs Juan produced).
($172.50) * (x - 2) = $198.00
Divide both sides of the equation by $172.50:
x - 2 = $198.00 / $172.50
x - 2 = 1.1478 (rounded to 4 decimal places)
Add 2 to both sides of the equation:
x = 1.1478 + 2
x ≈ 3.1478
Since you can't have a fraction of a CD, we round up the value of "x" to the nearest whole number.
Therefore, Juan produced approximately 4 CDs.