few problems...

[dimava]

I have a few problems that I need help with

[#9]

solve the system of equations
2x + (2/3)y = -8
1/2x - (1/3)y = 1

[#11]

Solve a system of equations to find the two numbers described.
The sum of two numbers is 17 and their difference is 29.

[#12]

The sum of a number and twice a greater number is 8. The sum of the greater number and twice the lesser number is -6.

[#16]

A boat travels 60 miles downstream in the same time it takes to go 36 miles upstream. The speed of the boat in still water is 15 mph greater than the speed of the current. Find the speed of the current.

[#36]

The geometric mean of a number and 3 is 9. Find the number: use  g = squareroot(ab)

[#50]

Al's flower garden measures 25 feet by 35 feet. He has enough crushed stone to cover 325 square feet. If he uses the stone to build a path around his garden, what is the maximum possible width of the path?

thanks in advance,

Dimava

[Electroman]

#9 add them together and it'll become clear

[Electroman]

#11:

a + b = 17
a - b = 29

#12:

a + 2b = 7
2a + b = -6

Thats all i'm doing, sounds like someones homework??

[sql_lall]

yes, does seem like homework
anyway, more hints:
#16)
speed of current = x
speed of boat in still water = x+15
=> speed upstream = (x+15)-x = 15
=> speed downstream = (x+15)+x = 2x+15

#30)
Geometric mean = sqrt(a*b) = 9
b=3. find a (come on, its trivial)

#50)
Let W = width
split the path into 8 section:
four corners of W x W, and 4 other rectangles.
Find the area of these reactangles, add them up, solve quadratic equation.

[dimava]

thanks for the replies..


for #50 I did the quadratic and I got X=-12.5 & X=-17.5, i'm not sure how to find the area with that.

[alkatran]

2x + (2/3)y = -8
1/2x - (1/3)y = 1

first things first, make the equations = each other:

isolate X (or Y)
2x = -8 - (2/3)y
1/2x = 1 + (1/3)y

now make them equal
2x = -8 - (2/3)y
2x = 4 + (4/3)y

so now since both = 2x we know that
-8 - (2/3)y = 4 + (4/3)y

now we isolate Y and solve
-8-4 = (4/3)y+(2/3)y
-12 = 2y
y = -6

then we use Y to find X
2x + (2/3)y = -8
2x + (2/3)-6 = -8
2x = -8 + 4
2x = -4
x = -2

[sql_lall]

ok, here's #50 in a bit more detail:
W=width of path
=> Area = 4W² + 2W(25-2W) +2W(35-2W)
(4 'corners' + the 4 remaining rectangles)

=120W - 4W² =325
=> 4W² - 120W + 325 = 0
=> [120 +/- 20sqrt(22)]/8
and you can get the answers from this

[Electroman]

Hehe I did the first one wrong you want to double the first one then do the first one minus the second, thats if you haven't already got the answer