SOLUTION: A shop had a total of 142 kg of rice and flour. After selling an equal amount of rice and flour, the amount of rice left was twice the amount of flour left. The amount of rice sold

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A shop had a total of 142 kg of rice and flour. After selling an equal amount of rice and flour, the amount of rice left was twice the amount of flour left. The amount of rice sold      Log On


   

Question 1204645: A shop had a total of 142 kg of rice and flour. After selling an equal amount of rice and flour, the amount of rice left was twice the amount of flour left. The amount of rice sold was 20 kg less than the amount of rice left. How much flour was sold ? How much rice was there at first?
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
MATERIAL         QUANTITY        QUANTITY Post-sale
Rice               r               r-x
Flour              f               f-x
Total              142

system%28r-x=2%28f-x%29%2Cx=r-x-20%2Cr%2Bf=142%29

************ REDONE***********

Questions are for finding r, and x. f can be substituted-for.

system%28r-x=2f-2x%2Cx=r-x-20%2Cr%2Bf=142%29

system%28r%2Bx=2f%2C2x-r=-20%2Cf=142-r%29, now sub. for f.

system%28r%2Bx=2%2A142-2r%2C2x-r=-20%29

system%283r%2Bx=284%2C-r%2B2x=-20%29
Use 3*E2.

system%283r%2Bx=284%2C-3r%2B6x=-60%29
ADD.
7x=224
highlight%28x=32%29---------------amount sold, of each

r-2x=20
r=2x%2B20
r=64%2B20
highlight%28r=84%29--------initial amount of rice, before selling any


Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

f = amount of flour left
2f = amount of rice left
x = amount of each item sold
f+2f+x+x = 142
3f+2x = 142

"The amount of rice sold was 20 kg less than the amount of rice left"
x = 2f - 20

3f+2x = 142
3f+2( x ) = 142
3f+2(2f-20) = 142
3f+4f-40 = 142
7f-40 = 142
7f = 142+40
7f = 182
f = 182/7
f = 26

x = 2f - 20
x = 2*26 - 20
x = 52 - 20
x = 32
2f+x = 2*26+32 = 52+32 = 84


Answers
32 kg of flour sold
84 kg of rice at first