Math 212- Word Story problems

Math word story problems

1. Phoenix is on a mission to prevent an underground drug deal involving the Japanese group The Hand. In order to prevent the deal from taking place, she must first locate Dr. Doom and his orderlies from reaching the meeting point for the exchange of goods. Phoenix has managed to locate a map with a set of coordinates for the direction she must go. However, this map only represents the Y axis she is following. Coordinates showing in the map are -5, -3, -1 0, 1, 3 and 5. Based on the Y axis information provided, if X= 2Y-3, figure out what are the values for the X axis and graph the result to determine which direction Phoenix must got to catch Dr. Doom.
2. News has spread that Joker is now dead. Harlequin has taken this opportunity to gain the ultimate power she longs for, however, before this occurs, she needs to capture servants to execute her rule. The first step in her plan is to capture Wolverine and brainwash him into being his servant as Horseman Death. Wolverine has already learned of this plan, and has taken flight across a map that has been laid out by Phoenix for him, and has been encoded into the equation 5x+3y=12. After Wolverine has taken flight, Harlequin has located Phoenix and has tortured her into confessing Wolverine’s whereabouts. Phoenix provided her with an incorrect path by giving him the equations 9x+15y=6, but she is unsure if these will lead Harlequin to Wolverine or not, Locate the slope of the equations and graph to determine if Harlequin and Wolverine cross paths.
3. Dr Doom has been hired to murder Wolverine. In an attempt to reach him in an unexpected situation, Dr. Doom has captured Wonder Woman and is keeping her hostage in an abandoned warehouse. He plans to use Wonder Woman as bait for Wolverine, to access the warehouse, and then explode it with Dynamite once they are both trapped inside. Dr. Doom needs 1 pound of dynamite for each 10 square feet of the warehouse. If the warehouse is 100 feet wide by 150 feet deep, how much dynamite will Dr. Doom need to use in order to efficiently blow up the warehouse and kill Wolverine and Wonder Woman?
4. Mystique is out on a personal vendetta against Phoenix. She has Phoenix captive and plans to drown her in a pool of mud. The pool is shaped as a prism, with a base of 15 ft and a height of 20 ft. Wolverine has set out to rescue Phoenix, but needs to hurry in order to get there in time to save her. If the pool fills up at the rate of 10 sq. foot per minute, determine how much time Wolverine has to save Phoenix before she drowns.
5. Dr. Doom has planted a bomb in the city of Equatus and plans to set it off and kill everyone in it. After much investigation, Wolverine has located the equation Dr. Doom has used to set the location of the bomb in the city: 9x+3y=12, and has also located one of the values needed to solve the equation: X=(-3). With this information, locate the coordinates for where the bomb is planted in order for Wolverine to save the city from destruction.
6. Harlequin, Joker and Mystique have teamed up in an effort to create chaos over the city of Equatus. They have set timed capsules that contain a deadly virus in 3 different points of the city, A, B and C, forming a right triangle. Point A is located 10 miles from point B. Point B is located 12 miles from point C. Locate the distance from point C to Point A, in order for Phoenix to be able to create a force field to protect the area and contain the virus in hopes to prevent humans contracting the virus and dying.
7. The Joker is out in the city for a day about town, however, what seems as an innocent stroll soon turns to chaos when the Joker and his minions are planning on firing on an open crowd in the town festival. Luckily, Phoenix happens to be at the festival herself, and is in a position where she can create a force field to protect the crowds. If the Plaza where the festival is happening has a length of 7 kilometers and a width of 5 kilometers, determine the area Phoenix must cover with her force field in order to protect the crowds.
8. Harlequin was trying to hold up a bank in the city, but she was unable to pull it off because Wolverine intervened in the situation. She ran off into the alleys of the city, and Wolverine is trying to locate her to have her turned into the police. He is able to locate the coordinates of his current location, (5,-4) and the location Harlequin was heading towards to (-1,8). Locate the slope of the line in order for Wolverine to know in which way he needs to go in order to capture Harlequin.
9. Phoenix is looking down through a factory at a 35˚ angle . If Harlequin is looking down at the same factory from an angle that would be the complementary angle to Phoenix, at what angle would Harlequin be standing at?
10. Wolverine needs to fun across the perimetre of the park in order to catch Dr. Doom before he tries to kidnap a young girl. If each of the park’s sides are 20 ft long, and the park is square, how many feet would Wolverine need to run in order to catch Dr. Doom?

Solution Sheet
1)
Y X
-5 -13
-3 -9
-1 -5
0 -3
1 -1
3 3
5 7

2)
a) 5x+3y=12
3y=(5x+12)/3
b) 9x=15y=6
15y= (9x+6)/15= (3x+2)/5
A and B are negative reciprocals, there for the lines intercept

3)1 pound of dynamite per 10 sq. Ft.
100ft +150ft=250ft
250ft/ 10sq ft.= 25 pounds of dynamite are needed


4)pool=prism
V=b*h
V=15ft * 20ft
V=300 sq. ft
300 sq. ft/ 10 sq. ft= 30 minutes before Phoenix drowns

5)9x=3y=12
X=(-3)
9 (-3) + 3y=12
-27+3y=12
3y=12+27
3y=39
Y=13
Coordinates are (-3,13)

6)C²= a²=+b²
C²=10²+12²
C=√244
C=15.62

7) A=b+h
A=7+5
A=35 ft. is the area Phoenix must cover to protect the crowds.
8) m=(y1-y1)/(x2-x1)=(-4-8)/5-[-1]) = -(12/6)
y-y1=m (x-x1)
y-(-4)=-2 (x-5)
y+4=-2x=10
y=-2x=6
9) A 55˚angle, because complementary angles complete 90˚
10)P=4b
P=4 (10)
P=40 ft.
Wolverine needs to run 40 ft. to catch Dr. Doom.