Math CentralQuandaries & Queries


Question from Dee:

In a previous question, you answered:

"What percentage of $34.51 is $10.71?

I translate this English statement into a mathematical statement (equation) using the following

"what" is the unknown, call it x
"percent" is per-one-hundred, that is over 100
"of" is multiplication
"is" is the verb, which in an equation is the equal sign
Thus the English statement above becomes

x/100 × $34.51 = $10.71

Solving for x yields

x = 31.03

Hence the gross profit is 31% of your selling price."

How did you solve for 'x'


Hi Dee,

I had the equation

x/100 x 34.51 = 10.71

Think of this as a balance with the balance point at the equal sign and the quantities on bath sides the same so that they balance. You want to manipulate both sides of the equation, always maintaining the balance and end with an equation of the form

x = some number.

I would first eliminate the fraction by multiplying both sides by 100. This will maintain the balance since you have multiplied both sides by the same amount, and yield

mult by 100

You can now cancel the two 100s on the left


to obtain

$34.51 x = $1071

Almost there. Finally divide both sides by $34.51 which will again maintain the balance and give

$34.51 x = $1071

Again there is cancellation on the left side, and division on the right yields

x = 31.03

I hope this helps,

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