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

 
 
CONCEPT QUESTIONS EXERCISE:
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.
PROBLEM TYPES:
1 2
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