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Linearequations/265006: At 11am, billy and leon set off towards each other from different places 32km apart. billy cycled at 20 km per hour and leon walked at 5km per hour.
draw distance time graphs of their journeys on the same grid to find out:
1. the time at which they met
2. the time at which they are 12km apart.
1 solutions
Answer 194976 by ankor@dixienet.com(18980) on 20100203 14:49:24 (Show Source):

Geometry_Word_Problems/263596: A piece of wire 40cm long is to be cut into two pieces. One piece wil be bent to form a circle; the other will be bent to form a square. Find the lengths of the two pieces that cause the sum of the area of the circle and square to be a minimum.
1 solutions
Answer 194300 by ankor@dixienet.com(18980) on 20100131 20:59:22 (Show Source):

Word_Problems_With_Coins/263282: A collection of 20 coins made up of only nickels, dimes and quarters has a total value of $3.35. If the dimes were nickels, the nickels were quarters and the quarters were dimes, the collection of coins would have a total value of $2.75. How many quarters are in the original collection?
1 solutions
Answer 194134 by ankor@dixienet.com(18980) on 20100131 14:28:17 (Show Source):
You can put this solution on YOUR website! Let the original number of coins be n, d, q
:
Write an equation for each statement:
:
"A collection of 20 coins"
n + d + q = 20
:
"made up of only nickels, dimes and quarters has a total value of $3.35."
.05n + .10d + .25q = 3.35
:
"If the dimes were nickels, the nickels were quarters and the quarters were dimes, the collection of coins would have a total value of $2.75."
.25n + .05d + .10q = 2.75
:
Multiply the above equation by 4, subtract from the 1st equation
1n + 1d + 1q = 20
1n +.2d +.4q = 11
subtraction eliminates n
.8d + .6q = 9
:
Multiply the 2nd equation by 20, subtract the 1st equation
1n + 2d + 5q = 67
1n + 1d + 1q = 20
subtraction eliminates n again
d + 4q = 47
:
Use elimination again on the these two, 2 unknown equations
Multiply the above equation by 4, multiply the 1st by 5, subtract it
4d + 16q + 188,
4d + 3q = 45
subtraction eliminates d, find q
13q = 143
q =
q = 11
:
How many quarters are in the original collection?
11 quarters originally

Travel_Word_Problems/263216: Bronwyn walks one lap of an oval at 2.5km/h and then jogs another 8 laps of the oval at 5km/h. If it takes her 30 minutes in total, how long in metres is each lap?
I am guessing that to work the answer out, simultaneous equations will need to be found.
In which case, I have figured that one of the simultaneous equations might be something like
5(8x) + 2.5(y) = 30 or something similiar, in which x stands for the distance covered when jogging, then multiplied by 8, the number of laps jogged, and then by 5, the speed at which it was jogged. And likewise for 2.5 and y.
1 solutions
Answer 194064 by ankor@dixienet.com(18980) on 20100131 10:13:20 (Show Source):

Expressionswithvariables/263223: The kinetic Energy (K) of a moving object varies jointly with its mass (m) and the square of its velocity (v). If an object weighing 90 kilograms and moving with a velocity of 20 meters per second has a kinetic energy of 4500 Joules, find its kinetic energy when the velocity is 32 meters per second.
1 solutions
Answer 193984 by ankor@dixienet.com(18980) on 20100130 22:00:24 (Show Source):

Age_Word_Problems/262873: The sum of the ages of three sisters, Carol, Cindy, and Lisa, is 42. Carol, the oldest, is 4 times as old as Lisa, who is the youngest. How old is Cindy? Explain how you know.
1 solutions
Answer 193962 by ankor@dixienet.com(18980) on 20100130 20:17:25 (Show Source):
You can put this solution on YOUR website! The sum of the ages of three sisters, Carol, Cindy, and Lisa, is 42.
Carol, the oldest, is 4 times as old as Lisa, who is the youngest.
How old is Cindy? Explain how you know.
:
let x, y, z = the three sisters, x is youngest, z the oldest
:
x + y + z = 42
:
The oldest (z) 4 times the youngest (x)
z = 4x
:
Replace z with 4x in the sum equation
x + y + 4x = 42
y + 5x = 42
y = 42  5x
:
Some values for this equation:
x  y

2 32
4 22
5 17
6 12
7  7
8  2
:
know y<4x and y>x, only two values for x will satisfy this:
x=5, y=17, z=20
and
x=6, y=12, z=24
:
Two solutions,
Cindy is age 17, or Cindy is age 12

