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Substance 1 contains 13% of A, 62% of B and 25% of C. Substance 2 contains 5% of A, 77% of B, and 18% of C. Substance 3 contains 29% of A, 13% of B, and 58% of C. How many parts of each to get 10% A, 50% B and 40% C? How do I solve this problem?

 Feb 16, 2021
 #1
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x = amount of 1       y = amount of  2    z= amount of 3         final amount = x+y+z

 

.13x   +   .05y    +   .29z    =    .1 (x+y+z)       This is for A

.62x    + .77 y    +  .13 z    =  .5 (x+y+z)          this is for B

.25x   +   .18y    + .58 z     = .4 (x+y+z)           this is for C

 

I think this is correct......I used wolfram alpha and got no answer !     This problem has no solution that I can fathom !

    Hope someone else can find an answer ....or the same conclusion !!!  cheeky

 Feb 17, 2021
 #2
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a=0;p=0; b=0;c=0;n=0.62*a    + 0.77*b    +  0.13*c +0.13*a   +   0.05*b    +   0.29*c+0.25*a   +   0.18*b    + 0.58* c  ;if(n==0.10*(a+b+c) + 0.50*(a+b+c) +0.4*(a+b+c), goto loop, goto next);loop:p=p+1;printp," =",a,b,c,n;next:a++;if(a<150, goto4,0);a=0;b++;if(b<150, goto4, 0);a=0;b=0;c++;if(c<150, goto4,0)

 

 

OUTPUT: By adding up the  3 equations, there appear to be many solutions such as:

 

a = 20,   b=140,   c=40

 Feb 17, 2021
 #3
avatar+29088 
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I'm a little confused....   are a,b,c  in your solution   corresponding to   Substance 1   2 and 3 ?

ElectricPavlov  Feb 17, 2021
 #4
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Take your first equation:

 

.13x   +   .05y    +   .29z    =    .1 (x+y+z)       This is for A

There are numerous solutions to x, y, z: 

such as x =70,  y = 80  and  z =10 . Sub these values for x, y, z and you get:

0.13 *70  + 0.05 * 80  + 0.29 * 10 =0.10*(70+80+10)

9.1            +     4             +      2.9      =0.10*(160)

                 16                                        =16

Guest Feb 17, 2021
 #5
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...of course there are numerous solutions for just ONE of the substances equations......but we are trying to mix substance A B and C to get the final substance of  10% A  50% B  and 40 % C     .....I don't believe there is a way to mix all three to get the final ....cheeky

   In other words....you only solved ONE of the equations......we need solve the SYSTEM of equations to find x y and z  that solves all THREE of the equations......

Guest Feb 17, 2021

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