Percent Problems
Asia has a pulse rate of 70
beats per minute. After
jumping rope, she increased
her pulse rate to 105 beats
per minute. She told her
friend Frank that her pulse
rate increased 25%. Is she
correct? Explain why or why
not. Justify using
mathematics.
105
x

meaning that her pulse rate increased by 50%.
70 100
105(100)  70x
10500 70x

70
70
150  x
105  70
x

70
100
35
x

70 100
or 35(100)  70x
3500  70x
3500 70x

70
70
50  x


Asia has a pulse rate of
70 beats per minute.
After jumping rope, she
increased her pulse rate
to 105 beats per minute.
She told her friend
Frank that her pulse rate
increased 25%.
Find 2 or more ways to solve the above problem.
Use the 2 ways above or the reasoning, “if 35 is half of 70 then half of 100 is 50.”
Great White Shark Population Census Study
What makes this Great White shark population census study particularly
significant is that it is the first rigorous scientific estimate of Great White shark
numbers in the northeast Pacific Ocean.
The Count
Researchers went to places in the Pacific Ocean where Great White sharks are known to
congregate. They lured the Great White sharks using a seal-shaped decoy on a fishing line, so the
sharks could be photographed close up. From 321 photographs of the uniquely jagged edges of
great white sharks’ dorsal fins, the team was able to identify 131 individual Great White sharks.
From this data, the scientists estimate that there are 219 adult and sub-adult Great White sharks in
the region. Great White sharks are classed as sub-adults when they reach about 8 feet to 9 feet in
length and when their dietary focus shifts from eating fish to mostly marine mammals. The Great
White sharks are then considered adults when they reach sexual maturity. For males, that is at
about 13 feet long; for females, it is when they reach approximately 15 feet long.
http://www.fishchannel.com/fish-news/2011/03/25/great-white-shark-population-censusstudy.aspx
1. What data is relevant to finding the approximate number of Great White sharks?
The data we need is 131 out of 321 and 219 out of x
2. Find the total number of Great White sharks in the northeast Pacific Ocean.
a.
131 219

321
x
321(219) = 131x
70299= 131x
536.6335 = x
which means about 537 total
3. What is your word ratio?
a. Number of sharks identified = Number of sharks that were adult or sub-adult
Total number of photographs Total number of sharks (babies, toddlers, etc.)
4. What is the percent of increase or decrease of Great White sharks in the northeast Pacific
Ocean if researchers estimated the total population of Great White sharks at 400?
a.


400  537
x

400
100
137
x

400 100
-13700 = 400x
-34.25 = x
The percent of decrease is 34.25%. The population of Great White sharks in the
northeast Pacific Ocean is 34% less than originally thought.
Great White Shark Population Census Study
What makes this Great White shark population census study particularly
significant is that it is the first rigorous scientific estimate of Great White shark
numbers in the northeast Pacific Ocean.
The Count
Researchers went to places in the Pacific Ocean where Great White sharks are known to
congregate. They lured the Great White sharks using a seal-shaped decoy on a fishing line, so the
sharks could be photographed close up. From 321 photographs of the uniquely jagged edges of
great white sharks’ dorsal fins, the team was able to identify 131 individual Great White sharks.
From this data, the scientists estimate that there are 219 adult and sub-adult Great White sharks in
the region. Great White sharks are classed as sub-adults when they reach about 8 feet to 9 feet in
length and when their dietary focus shifts from eating fish to mostly marine mammals. The Great
White sharks are then considered adults when they reach sexual maturity. For males, that is at
about 13 feet long; for females, it is when they reach approximately 15 feet long.
http://www.fishchannel.com/fish-news/2011/03/25/great-white-shark-population-censusstudy.aspx
1. People are considered teenagers when they are 13-19. When are Great White sharks
considered teenagers (sub-adults)?
a. When they are about 8 to 9 feet in length.
b. When they shift from eating fish to marine mammals.
2. What is the percent of increase or decrease in the length of a Great White male shark
from sub-adult (8 feet) to adult?
13  8
x

8
100
5
x

b.
8 100
a.

c. 8x = 500
d.
x = 62.5% increase in the size of a male Great White from sub-adult to adult.
3. What is the percent of increase or decrease in length of a Great White male shark from
sub-adult (9 feet) to adult?
13  9
x

9
100
4
x

b.
8 100
a.

c. 400 = 8x
d. 50 = x 50% increase in the size of a male Great White from sub-adult to adult.
4. What is the percent of increase or decrease when you used 8 and when you used 9 feet?
i. 62.5 – 50 = 12.5% increase in size. OR
b.

9 8
x

8
100
c.
d.

1
x

8 100
8x = 100 and x = 12.5% increase from 8 – 9 feet.