can not figure this out...

Question

The crew on a fishing boat caught four fish that weighed a total of 1092 pounds. The tarpon weighed twice as much as the amberjack and the white marlin weigh twice as much as the tarpon. The weight of the tuna was five times the weight of the amberjack. How much did each fish way?

Answer 1

OK, We are given the total weight of the 4 different fish = 1092 lbs

 

The weights are not given, only the ratios. Let's first define a variable for each fish by 2 letters.

 

TP = tarpon   AM = amberjack  WM = white marline  TN = tuna

 

now the ratios:

 

#1    TP   = 2*AM     (tarpon is 2x the amberjack)

#2    WM = 2*TP      (white marlin is 2x the tarpon)

#3    TN  = 5*AM     (tuna is 5x the amberjack)

 

since all but the WM is defined by a ratio of the AM we can define

WM = 2*TP = 2*(2*AM)     (since TP = 2*AM)  or

 

#4    WM = 4*AM

 

So, the 4 fish can be represented as ratios of AM, and their total = 1,092

 

1092 = TP + WM + TN + AM    (substituting the ratios of each below, we get:

 

1092 = 2*AM  +  4*AM  +  5*AM  + AM

 

1092 = 12*AM     so

 

AM  = 1092/12            = 91   (now just substitute the 91 LBS for AM in each eqns 1-4)

TP   = 2*AM   = 2*91   = 182

WM  = 4*AM  = 4*91   = 364

TN   = 5*AM = 5*91    = 455      

 

As a check, add each fish's weight. 

 

AM + TP + WM + TN  =  91+182+364+455 = 1,092 LBS

 

Answer 2

T = Tarpon

A = Amberjack

M = Marlin

N = Tuna

 

1) T + A + M + N = 1092

 

2) 2A = T

 

3) 2T = M

 

4) 5A = N

 

Just substitute formulas 2-4 into formula 1

T + A + M + N = 1092

2A  + A + 4A + 5A = 1092  [the 4A comes from the fact that M = 2T = 2(2A) = 4A]

12A = 1092

A = 91.  So the amberjack was 91 pounds.

 

Based on equation 2, we know the tarpon weighed twice the amberjack, or 182 pounds.

 

The marlin weighed twice the Tarpon, or 363 pounds.

 

The tuna weighed five times the amberjack, or 455 pounds.

 

Of course, this is a fish story, so it's probably all exaggerated.  : )

 

Hope this helps, Sarah!  If you never need online tutoring in math, let me know!