Word Problems- Linear and Stuffies.

[angelcircuit]

[USING LINEAR EQUATIONS]

Patricia lives in a house on a hill.
The grade of her street is 9%. The street ends at a river bank 360 yards from her front door.
Hector, Patricia's boyfriend, lives in a house 240 yards down from hers.
How much does the river level have to rise about the river bank to flood Hector's basement?
If Hector's house is 20 feet tall and the flood covers it completely, would Patricia's house suffer any flooding?
~i really could not understand the question~

[SOLVE USING A SET OF LINEAR EQUATIONS]

You have been hired by a group of anthropologists to sort out the data that they collected from a trip to Ja-Ji,
a remote island in the south Pacific. The people of Ja-Ji do not permit outsiders to count them directly: so, the
anthropologists had to collect all sort of other data to get to the population. They fear that they may have missed
something and your job is to make that assessment, or better yet, use what they have to get the population of Ja-Ji.
This is what their notes say:
People in Ja-Ji are either single or monogamous unions. 10% of the adult population of Ja-Ji is homosexual
and they are all in long term relationships. These homosexual unions constitute one fifth of the unions in Ja-Ji.
There are 1,000 children, which constitute half of the single population of Ja-Ji.
~~~I do not even know how to start this question~~~
_______________________________________________________________________________________________

A small private school has 500 students. two thirds of the soccer players are girls, two third of the boys play soccer.
one hundred of the girls do not play soccer. How many boys are in the school?

i have two solutions on this question, one is mine, and one is a friend's.

mine-->
*there are 500 students, but the question says ''one hundred of the girls do not play soccer''
*the question does not even state whether or not, the rest are all soccer players.
so this is what i came up with....
2/3 of the soccer players are girls, and 2/3 is 67% which is
67% of 400 is 268. and 400-268=132
~~132 is the total number of boys in the school.

But I was told to do it using independent linear equations. Which I cant figure out how.

 

[Denis]

[*there are 500 students, but the question says ''one hundred of the girls do not play soccer''
*the question does not even state whether or not, the rest are all soccer players.
so this is what i came up with....
2/3 of the soccer players are girls, and 2/3 is 67% which is
67% of 400 is 268. and 400-268=132
~~132 is the total number of boys in the school.
But I was told to do it using independent linear equations. Which I cant figure out how.

You're assuming and guessing...
2/3 is not 67%, it's 66 2/3 %: 2/3 of 400 = 266 2/3 : so that 266 girls + 2/3 of a girl ?!
And you're ending up with 400 girls and 132 boys; that's 532, but problem states only 500.

Assign variables: b = boys, g = girls, p = soccer players.
Then develop equations, like b + g = 500

That's something that requires teaching...so talk to your teacher.

 

[A_G]

Here's the first one:

Let x = height of Patricia's house above river level
Let y = height of Hector's house above river level.

"Grade" here means gradient meaning that for a distance of 100 yards horizontally, the height drops by 9 yards

So we have x/360 = y/(360-240) = y/240
=> x/3 = y/2 => 2x = 3y............(I)
Again, x/360 = 9/100..............(II)

Let us know if you can solve these equations from here on

Once you find 'x' and 'y' you need to check if 20 added to y exceeds x and comment on whether Patricia's house would suffer any flooding.

 

[TchrWill]

A small private school has 500 students. two thirds of the soccer players are girls, two third of the boys play soccer.
one hundred of the girls do not play soccer. How many boys are in the school?

Any luck yet? I looked at it this way:

1--Boys plus girls yields B + G = 500
2--B = sb + b (sb = soccer boys and b = non-soccer boys
3--G = sg + g = sg + 100 (sg and g similar to (2)
4--Sp = sb + sg (Sp = total of soccer players
5--(2/3)(sb + sg) = sg or sg = 2sb
6--(2/3)(sb + b) = sb or sb = 2b
7--B = 2sb + b = 3b
8--G = 2sb + 100 = 4b + 100
9--Can you take it from here?

I came up with a non-integer answer for b. Taking the nearest integer value, the totals add up to 499 students. Are there 101 non-soccer playing girls? Perhaps the 500th person is the coach. Let us know if you came up with 500 students.

 

[Denis]

Agree TchrWill: no integer solution.

Changing the 2 ratios from 66 2/3% to 62.5% and 60% would give an integer result:

t = total students (500)
r = girls not playing (100)
u = percentage of players who are girls (62.5 / 100)
v = percentage of boys who are players (60 / 100)
b = boys (?)
General case:
b = (t - r)(1 - u) / [1 - u(1 - v)]

b = (500 - 100)(1 - .625) / [1 - .625(1 - .6)] = 200