PROBLEMS INVOLVING PERCENT INCREASE AND DECREASE

Here, you will practice solving problems involving percent increase and decrease.
You may use a calculator for these exercises.

EXAMPLES:
Question:
Suppose an item costs $\,\$50\,$.
If the price increases by $\,19\%\,$, and then decreases by $\,30\%\,$, the new price is:
Solution:
$(0.7)(1.19)(\$50) = \$41.65$
Why?
To increase any amount by $\,19\%\,$, just multiply by $\,1.19\,$:
$\,x + 0.19x = 1x + 0.19x = 1.19x\,$
Notice that when you increase, you multiply by a number greater than $\,1\,$.
If you decrease any amount by $\,30\%\,$, then $\,70\%\,$ remains:
$x - 0.3x = 1x - 0.3x = 0.7x\,$
Thus, to decrease any amount by $\,30\%\,$, just multiply by $\,0.7\,$.
Notice that when you decrease, you multiply by a number less than $\,1\,$.
Combining these ideas:
$\$50$(original amount)
$(1.19)(\$50)$(new amount, after the $\,19\%\,$ increase)
$(0.7)\cdot (1.19)(\$50)$(new amount, after the $\,30\%\,$ decrease)
$(0.7)(1.19)(\$50) = \$41.65$(round dollar amounts (as needed) to two decimal places)

What if we switch the order of applying the increase/decrease?
$\$50$(original amount)
$(0.7)(\$50)$(new amount, after the $\,30\%\,$ decrease)
$(1.19)\cdot (0.7)(\$50)$(new amount, after the $\,19\%\,$ increase)
$(1.19)(0.7)(\$50) = \$41.65$(round dollar amounts (as needed) to two decimal places)
Same result!
Since $\,(1.19)(0.7) = (0.7)(1.19)\,$, you can do the multiplication in whatever order you prefer.
Question:
Suppose an item costs $\,x\,$.
If the price decreases by $\,38\%\,$, and then increases by $\,85\%\,$, the new price is:
Answer:
$(1 + 0.85)(1 - 0.38)(x) = (1.85)(0.62)x = 1.15x$
In this exercise, all answers are rounded to two decimal places.
Question:
Suppose an item costs $\,x\,$.
If the price decreases by $\,50\%\,$, and then increases by $\,50\%\,$, the new price is:
Answer:
$(1.5)(0.5)(x) = 0.75x$
Question:
Suppose an item costs $\,x\,$.
If the price increases by $\,50\%\,$, and then increases by $\,50\%\,$, the new price is:
Answer:
$(1.5)(1.5)(x) = 2.25x$
Question:
Suppose an item costs $\,\$100\,$.
If the price decreases by $\,50\%\,$, and then decreases by $\,50\%\,$, the new price is:
Answer:
$(0.5)(0.5)(x) = \$25.00$
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
More Problems Involving Percent Increase and Decrease

 
 
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
All answers are rounded to two decimal places.