Question 22·Easy·Percentages
A chemist needs to prepare 500 grams of a solution that is 60% sugar by weight. How many grams of sugar should the chemist use?
For SAT percent-of-a-quantity questions, first identify the whole (here, 500 g) and the percent of that whole (here, 60%). Convert the percent to a decimal by moving the decimal point two places left (60% → 0.60), then multiply: decimal × whole. Finally, do a quick reasonableness check: if the percent is less than 100%, your answer must be less than the whole; if it’s more than 50%, your answer should be more than half of the whole.
Hints
Identify what "60% sugar" refers to
Ask yourself: 60% of what? Is it 60% of the sugar, or 60% of the total solution mass (500 g)?
Rewrite the percent as a decimal
You need to work with 60% in a calculation. How do you write 60% as a decimal so you can multiply it by 500?
Set up the multiplication
Once you have the decimal form of 60%, multiply it by 500. Think: "decimal form of the percent" × "total grams of solution".
Desmos Guide
Use Desmos to compute 60% of 500
In Desmos, type 0.60*500 (or 0.6*500) on a new line. Look at the numerical output; that value is the number of grams of sugar needed.
Step-by-step Explanation
Translate the percent situation into math
The chemist wants a solution that is 60% sugar by weight, and the total solution should weigh 500 g.
That means: the mass of sugar should be 60% of 500 g. In math language, you are finding "60% of 500."
Convert the percent to a decimal
To work with a percent in an equation, convert it to a decimal.
- means out of .
- As a decimal, (or ).
So you need to calculate of grams.
Multiply to find the sugar mass
Now multiply the decimal form of the percent by the total mass:
.
So the chemist should use 300 g of sugar.