Math retardation (algebra)

[Regs]

I haven't practiced algebra in over 11 years and if wasn't for firefox I likely would not know how to spell the word .


The question is : "The perimeter of a rectangle is 96 meters. Three times the width is 8 meters less than length. What are the dimensions of the rectangle?"

How do I begin to solve this using the system of equations?
Obviously the rectangle has equal sides 2w and 2l...but I seem to have trouble finding the relationship with w = 8 - L.

 

[rcpratt]

3w = l - 8
2l + 2w = 96

Solve for w or l in the first equation and substitute into the second would be the most straight-forward way.

 

[CLite]

(1) w + L = 48
(2) L = 3w + 8
subsitute for L into (1)
w + (3w + 8) = 48
w = 10
L = 38

 

[Dumac]

2w=W + 2L = 96
3W = L-8

SOLVE

EDIT: All you have to do with word problems like these is convert the sentences into equations.

 

[MrPickins]

Systems of linear equations are damn useful.

I'm glad I took linear algebra...

 

[Crusty]

1) Reduce equations to upper row-echelon form
2) Perform Gaussian Elimination
3) Enjoy solutions

 

[rcpratt]

Linear algebra solutions are clearly the easiest way to explain an algebra II level problem.

 

[summit]

I haven't practiced algebra in over 11 years and if wasn't for firefox I likely would not know how to spell the word .


The question is : "The perimeter of a rectangle is 96 meters. Three times the width is 8 meters less than length. What are the dimensions of the rectangle?"

How do I begin to solve this using the system of equations?
Obviously the rectangle has equal sides 2w and 2l...but I seem to have trouble finding the relationship with w = 8 - L.

sides are g and h

first equation 96= 2g +2h
second 3g= h+8

multiply both sides of second equation by -2
-6g= -2h-16
16= -2h+6g

solve for g
112= 8g
g= 14

plug into second equation
14(3)= h+8
42= h+8
h=32

check your solution 32+32+14+14 = 64+28 = 96

 

[Regs]

Hm what about 2(3w+8) + 2w = 96 ? If I use the sub method I get w= 10 and L = 38

Does that "satisfy" the problem?

 

[MrPickins]

sides are g and h

first equation 96= 2g +2h
second 3g= h+8

multiply both sides of second equation by -2
-6g= -2h-16
16= -2h+6g

solve for g
112= 8g
g= 14

plug into second equation
14(3)= h+8
42= h+8
h=32

check your solution 32+32+14+14 = 64+28 = 96

Three times the width is 8 meters less than length.

CLite already had it.

 

[Regs]

CLite already had it.

Ah yes! Math is so fun.

You guys should try finance.

 

[Turin39789]

3 -1 -8
2 2 96