   SEARCH HOME Math Central Quandaries & Queries  Question from Tyler: if 45% of an item is $90.00,$ then what is the original price Hi Tyler,

If possible I like to have some idea of the size of the answer before I start. In this case 45% is slightly smaller that 50% so what if the problem were "if 50% of an item is $90.00, then what is the original price". 50% is one-half so if one-half of the item was$\$90.00$ then the original price would be $\$180.00.$So the answer to your problem is somewhat more than$\$180.00.$

What did I do here? I had

$\frac{1}{2} \mbox{ of the original price is 90 dollars}$

I can read this as an equation where the word "is" is the equal sign. Then I multiplied each side by 2 to get

$\mbox{ the original price is } 2 \times 90.00 = 180.00 \mbox{ dollars.}$

45% is also a fraction, it's $\large \frac{45}{100}$ So your question can be seen as

$\frac{45}{100} \mbox{ of the original price is 90 dollars}$

This time you need o multiply each side of the equation by $\large \frac{100}{45}$ to get

$\mbox{ the original price is } \frac{100}{45} \times 90.00 \mbox{ dollars.}$     