SME
Grade 7 Math · Problem type
Percent increase and decrease
Use this for “The price went from 50¢ to 60¢. What is the percent increase?” or “After a 25% increase it costs $50. What was the original price?”
Diagram
50 − 40 = 10
10 ÷ 40 = 25%
An increase of 25%
This is an example. Type your own values to start a new problem.
a
−
b
=
c
c
÷
b
×
100
=
p
%
Formulas
c
=
a
−
b
(change
=
new
amount
−
original
amount)
10 = 50 − 40
p
=
c
÷
b
×
100
(percent
change
=
change
÷
original
amount
×
100)
25 = 10 ÷ 40 × 100
a
=
b
×
(1
+
p
÷
100)
(new
amount
=
original
amount
×
(1
+
percent
change
÷
100))
50 = 40 × (1 + 25 ÷ 100)
Assumptions
•
The change is the new amount minus the original; it is negative for a decrease.
•
Percent change = change ÷ original × 100: always divide by the original.
•
A 20% increase then a 20% decrease does not bring the price back.
Step-by-step
WE KNOW
b = 40 (original amount), a = 50 (new amount)
FIND
change (c), percent change (p)
Step 1 · Find change (c)
Use c = a − b (change = new amount − original amount)
Take the original from the new amount.
c
=
50
−
40
c
=
10
Step 2 · Find percent change (p)
Use p = c ÷ b × 100 (percent change = change ÷ original amount × 100)
Divide the change by the original, then × 100.
p
=
10
40
×
100
p
=
0.25
×
100
p
=
25%
Check
Put the numbers back in. Both sides should match.
10 = 50 − 40 ✓
25 = 10 ÷ 40 × 100 ✓
50 = 40 × (1 + 25 ÷ 100) ✓
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