VIC's Chapter 4: Formulas Problem Set quest 10

by **kimd6746** Sat Apr 12, 2008 7:09 pm

Hello,

I'm totally confused by question 10 in pg 61's Problem Set. The answer says that the relationship between Wa=4Wb and A=256. Why should 4 be multiplied to Wb when the question says that "the team won 1/4 as many games in year B as it did in year A....". Shouldn't it read Wa=.25Wb? What am I missing?

by **RonPurewal** Wed Apr 16, 2008 4:33 am

nope, you've got it backwards.

here's the best way to figure it out: just think about which of the two values is bigger, and create an equation reflecting that choice.

in this case, the statement you've quoted definitely means that the team won more games in year A. therefore, you must write an equation that makes Wa a bigger number than Wb.
check the possible equations you could write:
Wa = 4Wb --> good (Wa is bigger)
Wb = 4Wa --> bad (Wb is bigger)
Wa = 0.25Wb --> bad (Wa is smaller)
Wb = 0.25Wa --> good (Wb is smaller)

this is ultimately easier than trying to memorize algebraic translations of every possible combination of words under the sun. but hopefully you've learned the following lesson: just because a number is closer to a given word in a statement, doesn't mean that number will appear next to the variable representing that word in the equation you eventually write.

i hope that last sentence makes sense; it's definitely one of those things that's easier to say out loud than to type on a forum.

by **UPA** Mon Apr 28, 2008 11:44 pm

kimd6746 Wrote:Hello,

I'm totally confused by question 10 in pg 61's Problem Set. The answer says that the relationship between Wa=4Wb and A=256. Why should 4 be multiplied to Wb when the question says that "the team won 1/4 as many games in year B as it did in year A....". Shouldn't it read Wa=.25Wb? What am I missing?

what is VIC's?

by **StaceyKoprince** Mon Apr 28, 2008 11:52 pm

The full name of the book is Equations, Inequalities and VICs. VIC is a specific technique for solving certain kinds of algebra problems.

by **kimd6746** Sun May 04, 2008 6:57 pm

I'm still having trouble with this question. The answer in the book is as follows:

Let a = comp edge yr A
Let b = comp edge yr B

Wa = 4 Wb
A = 256B

It then tells you to cross multiple the following algebraic expression given the Comp Edge formula of W^3/L^2.

((4Wb)^3)/(La^2) = (256Wb^3)/(Lb^2)
begats:
64WbLa^2 = 256Wb^3La^2
begats:
Lb^2 = 4La^2
Lb = 2La

My question is, why wasn't 256Wb raised to the 3rd power like 4Wb^3 (eg. 64WbLa^2) has? I know raising 256 to the 3rd power will give you a crazy number, but on principle shouldn't you follow the same power rules on both sides?

by **RonPurewal** Sun May 11, 2008 12:34 am

kimd6746 Wrote:My question is, why wasn't 256Wb raised to the 3rd power like 4Wb^3 (eg. 64WbLa^2) has? I know raising 256 to the 3rd power will give you a crazy number, but on principle shouldn't you follow the same power rules on both sides?

1)
standard order of operations says no: if i write the expression 256w^3, then that means you should first cube 'w', and then multiply the resulting quantity by 256.

2)
moreover, you know that you are multiplying last year's formula by 256. this means that the multiplication by 256 must be done last, anyway - regardless of order of operations - because the context of the problem makes it clear that you are calculating the formula for last year, and then multiplying it by 256.

make sense?

by **Guest** Sat Jan 31, 2009 2:55 pm

I don't understand how 256Wb^3 came from.

I understand that A=256 Band I understand why (4Wb) was substituted for Wa, but I just don't understand how the Wb got the 256.

by **bump** Tue Feb 03, 2009 11:40 pm

by **esledge** Sun Feb 22, 2009 3:37 pm

First, just a reminder that we answer questions according to date (older first), giving some priority given to current students. When you "bump" a question, you give it a later date, causing it to lose its place in line and be answered later as a result.

Guest Wrote:I don't understand how 256Wb^3 came from.

I understand that A=256 Band I understand why (4Wb) was substituted for Wa, but I just don't understand how the Wb got the 256.
I don't understand how 256Wb^3 came from.

I understand that A=256 Band I understand why (4Wb) was substituted for Wa, but I just don't understand how the Wb got the 256.

Here's all the steps:

Variable definitions
W = # of wins
L = # of losses
"edge" = (W^3)/(L^2)
A = "edge" of the team in year A = (Wa^3)/(La^2)
B = "edge" of the team in year A = (Wb^3)/(Lb^2)

Given formulas
A = 256(B)
Wb = (1/4)Wa
We want to solve for % increase in losses: % change from La to Lb.

Manipulation of formulas
A = 256(B)
(Wa^3)/(La^2) = 256(Wb^3)/(Lb^2) {substitution of both "edge" definitions...this is where Wb "got" the 256.}
(Wa^3)*(Lb^2) = 256(Wb^3)*(La^2) {cross-mulitplying}
(Wa^3)*(Lb^2) = 256((1/4)Wa)^3*(La^2) {substituting (1/4)Wa for Wb--given formula}
(Wa^3)*(Lb^2) = (256/4^3)*(Wa^3)*(La^2) {manipulating the constants}
(Wa^3)*(Lb^2) = 4*(Wa^3)*(La^2) {manipulating the constants}
(Lb^2) = 4*(La^2) {canceling Wa^3 from both sides}
Lb = 2*La {square root of both sides}

Double the losses in B means an increase of 100% from losses in year A.