A prize for a computer contest includes a computer worth 1/2 of the value of the prize, a monitor worth 1/2 of the remaining value, a modem worth $200, and software worth $150. What is the total value of the prize.
This is so challenging, I need help.
.5 x + .25 x = monitor + modem
.25 x remains
so
.25 x = 200 + 150
To find the total value of the prize, we'll need to calculate the value of each individual component and then add them together.
Let's break it down step by step:
1. The computer is worth 1/2 of the value of the prize. So, if we assign the value of x to the prize, the computer's value would be x/2.
2. The remaining value, after accounting for the computer, is also worth 1/2. So, the monitor's value would be (x - x/2)/2, which simplifies to x/4.
3. The modem has a fixed value of $200, regardless of the prize's total value.
4. Similarly, the software has a fixed value of $150, regardless of the prize's total value.
Now, we can add up the values to find the total value of the prize:
x/2 + x/4 + $200 + $150
To simplify the expression, we need to find a common denominator for the first two terms. The common denominator of 2 and 4 is 4, so we'll rewrite the expression as follows:
(2x/4) + (x/4) + $200 + $150
Combining like terms, we have:
(3x/4) + $200 + $150
Now, we can plug in any arbitrary value for x to find the total value of the prize. For example, let's say x = $800:
(3 * $800)/4 + $200 + $150
($2400/4) + $200 + $150
$600 + $200 + $150
$950
Therefore, if the value of the prize is $800, the total value of the individual components would be $950.