Expert: Sherry Wallin - 11/28/2009

Question
The nominal family took a trip to an apple orchard and picked 4 different types of apples.Fuji,Cortland, Braeburn,and Rome.When done they noticed they had atotal of 360 apples.There were two times as many Braeburn as Fuji, There were two times as many Cortland as Rome,and there were 50% more Fuji than Rome.How many of each apple did they pick?

Answer
Jacinta~
 
Let f = # of Fuji apples; c = # of Cortland apples; b = # of Braeburn apples; r = # of Rome apples

you know that f + c + b + r = 360 -> total apples picked was 360

b = 2f -> there were twice as many Braeburn as Fuji-> b-2f = 0

c = 2r -> there were twice as many Cortland as Rome -> c -2r = 0

r = 1.5f -> (f + .5f = 1.5f)there were 50% more Fuji than Rome -> r - 1.5f = 0

from the given information


this is a system of 4 linear equations in 4 variables, i.e., a solvable system

   f +  c +  b +  r = 360  (eqn #1) c = 2r so substitute 2r into (#1) for c -> f + 2r + b + r = 0
 -2f         b      = 0    (eqn #2) b = 2f so substitute 2f into (#1) for b -> f + 2r + 2f + r = 0
        c       -2r = 0    (eqn #3)
-1.5f              r = 0    (eqn #4) r = 1.5f sub. 1.5f into (#1) for r -> f+2(1.5f)+2f+1.5f = 360



f+2(1.5f)+2f+1.5f = 360 -> f + 3f + 2f + 1.5f = 7.5f = 360 so f = 360/7.5 -> f = 48
now put f = 48 into (eqn #2): -2(48) + b = 0 -> b = 96
use f = 48 into (eqn #4): -1.5(48) + r = 0 -> r = 72
and finally you just need c,use eqn #1: 48 + c + 72 + 96 = 360 ->c = 144(you could have used eqn 3)

So there were 48 Fuji, 96 Braeburn, 72 Rome and 144 Cortland apples picked

Math Prof