A factory’s total annual expenses are five million dollars. 40 percent of which goes into buying materials needed for manufacturing and 30 percent goes into paying the workers’ wages. If the cost of buying wood represents 25 percent of the cost of all purchased materials, what is the cost of buying the rest of the materials?
We need to calculate the cost of the rest of the materials. We can break the materials into two groups, wood and everything else. If wood represents 25 percent of the cost of materials, everything else is represented by 75 percent of the cost of materials. At this point, we need to go back and find out how much money we’re spending on all the materials together. They spent five million on expenses. 40 percent of that goes into materials. To multiply five million by 40 percent, I write 40 percent as a decimal and multiply five times 0.40, which gives the number two.
We’re still working in millions. The factory spends two million on materials. And of that two million, the rest of the supplies account for 75 percent of it. So we need to multiply two by 75 percent. So we multiply two by 0.75. You could also multiply two times three-fourths. 75 percent written as a fraction is three-fourths. Two times 0.75 equals 1.5. Two times three-fourths equals six-fourths or one and a half. The factory must spend one and a half million dollars on the materials that are not wood. If we write 1.5 million out, it becomes 1500000 dollars as half a million is 500000. So the cost of buying the rest of the materials is 1500000 dollars.
We can also note that it’s possible to solve this problem in one step. Five million times 40 percent written as a decimal, 0.40, and then multiplied by 0.75. Because every step is multiplication, we can do that all at once. And it gives 1.5, which is 1500000 dollars.