Mike spent $832 building a computer. The expenses included software, hardware, and peripherals. He spent 60 percent more for the hardware than for the software and peripherals combined.
How much did Mike spend on the hardware?
Although there are three categories, we can generalize this problem to just two - the hardware and everything else. Because the hardware costs 60% more than the software and peripherals combined,
$$ \text{Hardware} = \text{software and peripherals}+ \text{software and peripherals} \cdot 60\% $$
The previous equation can also be written like the following, using \(H\) for hardware and \(E\) for everything else.
$$ H=E(1+0.60) $$
$$ H=1.6E $$
We also know that the total price is $832, allowing us to write a general equation for the total.
$$ H + E = 832$$
Substituting \(H=1.6E\) into this equation.
$$ 1.6E + E = 832 $$
$$ 2.6E = 832 $$
$$ E = 320 $$
Plugging this back into the general equation for the total:
$$ H + 320 = 832 $$
$$ H = \boxed{512} $$
Test the answer choices. The cost of the hardware should be 60% more than the cost of the software and peripherals combined. We can eliminate the first two choices because they are less than half of the total cost, which won't make sense since the hardware is supposed to be more expensive than the other parts.
Using option 3:
$$ \text{Hardware} = 512 $$
$$ \text{Software and Peripherals} = 832-512 = 320 $$
Testing if it's 60% more:
$$512 = 320 \cdot \text{(percent change)}$$
$$ \frac{512}{320}=\text{(percent change)} $$
$$ 1.6 = \text{(percent change)} \checkmark $$
1.6 when converted to percents is 160%, or a 60% increase.