To solve for the total price [tex]\( t \)[/tex] of the computer, we start with the given formula:
[tex]\[ x = t - yz \][/tex]
Here:
- [tex]\( x \)[/tex] is the down payment amount.
- [tex]\( y \)[/tex] is the money paid each month.
- [tex]\( z \)[/tex] is the number of months.
- [tex]\( t \)[/tex] is the total price of the computer.
We need to rearrange the formula to solve for [tex]\( t \)[/tex].
Step 1: Start with the original equation:
[tex]\[ x = t - yz \][/tex]
Step 2: Isolate [tex]\( t \)[/tex] by adding [tex]\( yz \)[/tex] to both sides of the equation:
[tex]\[ x + yz = t \][/tex]
Step 3: Rewrite the equation to explicitly solve for [tex]\( t \)[/tex]:
[tex]\[ t = x + yz \][/tex]
Now plug in the given placeholder values to find the total price:
- The down payment [tex]\( x \)[/tex] is [tex]$100.
- The amount paid each month \( y \) is $[/tex]50.
- The number of months [tex]\( z \)[/tex] is 10.
Substitute these values into the equation:
[tex]\[ t = x + yz \][/tex]
[tex]\[ t = 100 + (50 \times 10) \][/tex]
[tex]\[ t = 100 + 500 \][/tex]
[tex]\[ t = 600 \][/tex]
Therefore, the total price [tex]\( t \)[/tex] of the computer is [tex]\( 600 \)[/tex] dollars.
