Percent of increase/decrease: write an equation to solve for the original price

First I show how to write a simple expression for the new price when we know the percent of increase or decrease. For example, 0.8 × $18 tells us the new price if a $18 shirt is discounted by 20% (because in that case, 80% of the price is left). And 1.08 × $34 tells us the new price after a $34 water bill is increased by 8%. Notice we use DECIMALS instead of percentages in these expressions.

Then we use simple equations to solve some percentage problems. If a shirt is discounted by 35% and the discounted price is $9.95, what is the new price? We can write the equation 0.65p = $9.95 and solve that to find out.

Lastly I solve a similar problem concerning a price increase.

See also

Percentage of change — video lesson

Math Mammoth Grade 7 curriculum (pre-algebra)

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