SOLUTION: Should this all be converted to decimals? Unable to solve this one. Mark's weight is 110% of Steve's weight. The ratio of Joseph's weight to Tim's weight is 10 : 11. The ratio

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Should this all be converted to decimals? Unable to solve this one. Mark's weight is 110% of Steve's weight. The ratio of Joseph's weight to Tim's weight is 10 : 11. The ratio      Log On


   

Question 585374: Should this all be converted to decimals? Unable to solve this one.
Mark's weight is 110% of Steve's weight.
The ratio of Joseph's weight to Tim's weight is 10 : 11.
The ratio of Carl's weight to Mark's weight is 6 : 7.
Carl's weight is 120% of Joseph's weight. Who weighs the least?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
let their weights =
Mark's = +m+
Steve's = +s+
Joseph's = +j+
Tim's = +t+
Carl's = +c+
------------
To convert decimals, move decimal point
2 places to the left
given:
(1) +m+=+1.1s+
(2) +j%2Ft+=+10%2F11+
(3) +c%2Fm+=+6%2F7+
(4) +c+=+1.2j+
-----------
Normally you couldn't solve this for all
their weights because there are 5 unknowns
and only 4 equations.
They only want the one who weighs the least,
so I can find that.
-----------
(3) tells me Mark weighs more than Carl
(4) tells me Carl weighs more than Joseph
So far the order is
Mark
Carl
Joseph
Now substitute (1) into (3)
(3) +c%2Fm+=+6%2F7+
(3) +c%2F%281.1s%29+=+6%2F7+
(3) 7c+=+6%2A1.1s+
(3) +c%2Fs+=+%286.6%2F7%29+
So, Steve weighs more than Carl, but (1)
says Mark weighs more than steve, so
the order now is
Mark
Steve
Carl
Joseph
------------
(2) says Tim weighs more than Joseph
No matter where Tim fits in, Joseph Has
to weigh the least
Hope I got it