1. Exercise
Specify what the variable stands for, write an equation, and solve. Be sure to label your answer.

2. Exercise
Jerry swam for twice as long as he ran and biked for three times as long as he ran. If his total exercise time was two hours, how long did he run?
x = the time he ran
2x + 3x + x = 120
x = 20 min.

3. Exercise If Jerry ran at a pace of 9 mi./hr., how far did he run?
d = the distance
d = 9( )
1 3
d = 3 mi.

4. Percent Formula
The percent of the whole is equal to the part: percent x whole = part.

5. Steps to Solving Problems with Equations
Represent an unknown quantity with a variable.
When necessary, represent other conditions in the problem in terms of the same variable.

6. Steps to Solving Problems with Equations
3. Identify two equal quantities in the problem.
4. Write and solve an equation.

7. Example 1
Of the 430 delegates, only 350 showed up due to the bad weather. What percent were able to attend? Round to the nearest tenth of a percent.
Let p = the percent.
percent x whole = part

8. 81.4% of the delegates were able to attend.
Of the 430 delegates, only 350 showed up due to the bad weather. What percent were able to attend? Round to the nearest tenth of a percent.
p = …
430p = 350
p ≈ 81.4%
430
81.4% of the delegates were able to attend.

9. Example 2
There are 200 kg of a metal alloy known to be 60% zinc. How much zinc does the alloy contain?
Let z = the amount of zinc.
percent x whole = part
0.6(200) = z
z = 120
It contains 120 kg of zinc.

10. Example 3
Find the monthly income of the Oliver family if their monthly mortgage payment of $840 represents 21% of their monthly income.
Let m = the monthly income.
percent x whole = part

11. The Olivers’ monthly income is $4,000.
Find the monthly income of the Oliver family if their monthly mortgage payment of $840 represents 21% of their monthly income.
0.21m = 840
m = 4,000
0.21
The Olivers’ monthly income is $4,000.

12. Example
What percent of a mixed nut package is peanuts, if at the plant 500 lb. of peanuts are added to 750 lb. of other nuts?
40%

13. Example
Historically 35% of freshmen have qualified to take honors Algebra I. How many are expected to take the class next year if the freshman enrollment is 160?
56 freshmen

14. Example
If the price of gasoline rose 22% from $2.77/gal., what is the new price?
$3.38/gal.

15. Example
If 12 oz. of a 64 oz. bottle of apple drink is actual apple juice, what percent is this?
18.75%

16. whole
100%
60%
40%
100%

17. Example 4
Only 24% of the registered voters participated in the last election. How many of the 33,000 registered voters did not cast a vote?
Let n = number of non-voters.
n = 0.76(33,000)
n = 25,080
25,080 did not vote.

18. Example 5
The 2,256 in attendance left 6% of the seats in the auditorium vacant. Determine the seating capacity.
Let s = the number of seats.
0.94s = 2,256
s = 2,400
0.94
There are 2,400 seats.

19. whole
20%
100%

20. Example 6
The cost of a large beverage is 40% more than the cost of a small beverage. Determine the price of the large drink if the small costs $0.95.
Let l = cost of the large drink.
l = 1.4(0.95)
l = $1.33
The large drink costs $1.33.

21. Example
If a car radiator can hold 5 gal. and currently contains 4 gal. that is 20% antifreeze, what will the percentage of antifreeze be after 1 gal. of pure water is added?
16%

22. Example
A chemist adds 100 mL of pure (100%) hydrogen peroxide to a 100 mL solution that is 5% hydrogen peroxide. What is the percentage of hydrogen peroxide in the mixture?
52.5%