Question 235827
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Let *[tex \Large r] represent the number of red marbles.  Let *[tex \Large m] represent the total number of marbles.


We are given that


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ r\ =\ \frac{m}{3}]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ r\ +\ 1\ =\ \frac{3}{8}(m\ +\ 1)]


Because if you increase the number of red marbles by 1, you have also increased the total number of marbles by 1.


Equivalent expressions:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ 3r]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3m\ +\ 3\ =\ 8r\ +\ 8]


Substituting:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 9r\ +\ 3\ =\ 8r\ +\ 8]


Solve for *[tex \Large r], then multiply by 3 to get *[tex \Large m], then subtract *[tex \Large r] from *[tex \Large m]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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