21 is 75 percent of a number. Find the number.
There are a couple of ways we can
tackle this problem. For the first method, let’s begin
by imagining we know what the starting number was. We’ll call that 𝑥. If we did know the starting number,
we could calculate 75 percent of it by finding the decimal multiplier that
corresponds to 75 percent.
Since “percent” means “out of 100,”
we can find the decimal multiplier by dividing 75 by 100. 75 divided by 100 is 0.75. To find 75 percent of our starting
number 𝑥 then, we multiply 𝑥 by 0.75. We know that that gives us an
answer of 21.
Notice now we formed a linear
equation, which we can solve to work out the value of 𝑥. We solve by performing the inverse
operation. Remember, that’s the opposite. The opposite of multiplying by 0.75
is dividing by 0.75. So to solve this equation, we’ll
divide both sides by 0.75. 𝑥 is going to be found by dividing
21 by 0.75, which gives us a starting number of 28.
The second method involves
scaling. We know that 21 is equal to 75
percent of the number. To find the original number, we
want to work out what 100 percent is. We can’t easily get straight from
75 to 100, but we can divide 75 by three to get 25, which is a factor of 100. 21 divided by three is seven, so
that means seven must be 25 percent of the original number. To scale 25 percent back up to 100,
we’ll need to multiply by four. Seven multiplied by four is 28, so
once again we’ve shown that the original number is 28.
Whichever method we choose, we can
check our answer by calculating 75 percent of 28. If the answer to that is 21, then
the chances are that we’ve calculated our number correctly. The number is 28.