SOLUTION: Cheryl gives 1/2 of her marbles to Alisha, 1/5 of her marbles to Linda, and 1/6 of her marbles to Nina. Cheryl is left with 40 marbles. How many did she start with? 36 Student

Algebra ->  Percentages: Solvers, Trainers, Word Problems and pie charts -> SOLUTION: Cheryl gives 1/2 of her marbles to Alisha, 1/5 of her marbles to Linda, and 1/6 of her marbles to Nina. Cheryl is left with 40 marbles. How many did she start with? 36 Student      Log On


   

Question 1186037: Cheryl gives 1/2 of her marbles to Alisha, 1/5 of her marbles to Linda, and 1/6 of her marbles to Nina. Cheryl is left with 40 marbles. How many did she start with?

36 Students got As; 1/3 got Bs; 1/5 got Cs; 1/6 got less than C. How many students took the test?
Found 2 solutions by JBnovelwriter, MathTherapy:
Answer by JBnovelwriter(34) About Me  (Show Source):
You can put this solution on YOUR website!
this is all bout common denominators
(2)(5)(6)=60
so where x = total amount of marbles
%2830%2F60%29x=A
%2812%2F60%29x=L
%2810%2F60%29x=N
Currently %2852%2F60%29x is given away, meaning %288%2F60%29x=C
and C=40
%288%2F60%29x=C
%288%2F60%29x=40 simplify
%282%2F15%29x=40 multiply by reciprical
x=40%2815%2F2%29 cross cancel out 2
x=20%2815%2F1%29 multiply
highlight%28x=300%29
36 Students got As; 1/3 got Bs; 1/5 got Cs; 1/6 got less than C. How many students took the test?
this question is the same thing
this is all bout common denominators
(3)(5)(6)=90
so where x = total amount of students
Known from problem:
A=36
B=%2830%2F90%29x
C=%2818%2F90%29x
D=%2815%2F90%29x
A%2BB%2BC%2BD=x
add up B%2BC%2BD=%2863%2F90%29x
this means A=%2827%2F90%29x
A=36
36=%2827%2F90%29x simplify by removing 9/9 from fraction
36=%283%2F10%29x multiply by reciprical
36%2810%2F3%29=x cancel out the 3/3
12%2810%2F1%29=x multiply
highlight%28120=x%29

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

Cheryl gives 1/2 of her marbles to Alisha, 1/5 of her marbles to Linda, and 1/6 of her marbles to Nina. Cheryl is left with 40 marbles. How many did she start with?

36 Students got As; 1/3 got Bs; 1/5 got Cs; 1/6 got less than C. How many students took the test?
1)Given away:  of total number of marbles
 
Fraction that remained: matrix%281%2C3%2C+1+-+13%2F15%2C+%22=%22%2C+2%2F15%29
Number of marbles that remained: 40

          We then get: matrix%281%2C3%2C+%282%2F15%29%2F1%2C+%22=%22%2C+40%2FM%29, with M being the original number of marbles

                       matrix%282%2C3%2C+2M%2F15%2C+%22=%22%2C+40%2C+2M%2C+%22=%22%2C+15%2840%29%29 ------ Cross-multiplying

Number of marbles, or