Question 259815
Let C = colored, and S = solid
We create two equations from the given
(i) {{{S + C = 40}}}
(ii) {{{9.90S + 12.75C = 421.65}}}
First get rid of the decimals in (ii) and write
(iii) {{{990S + 1275C = 42165}}}
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step 1 - solve (i) for S and we get
(iv) {{{C = 40-S}}}
step 2 - substitute (iv) into (iii) to get
(v) {{{990S + 1275(40-S) = 42165}}}
distribute and simplify to get
(vi) {{{-285S + 51000 = 42165}}}
subtract to get
(vii) {{{-285S = -8835}}}
divide to get
{{{S = 31}}}
so, we have
{{{C = 9}}}