Write equations for each succeeding sentences. Use G for green, B for blue, and W for white beads.
[tex]\begin{gathered} G+B+W=1350 \\ G=2B \\ W=\frac{1}{2}(G+B) \\ G=\text{?} \end{gathered}[/tex]Solve for the value of G as follows.
Rewrite the equations in terms of B. Since the value of G is already written in terms of B, write the value of W in terms of B.
[tex]\begin{gathered} W=\frac{1}{2}(G+B)_{}_{} \\ =\frac{1}{2}(2B+B) \\ =\frac{1}{2}(3B) \end{gathered}[/tex]Substitute the values of G and W, in terms of B, into the first equation and then solve for B.
[tex]\begin{gathered} G+B+W=1350 \\ 2B+B+\frac{1}{2}(3B)=1350 \\ 4B+2B+3B=2700 \\ 9B=2700 \\ B=300 \end{gathered}[/tex]Note that we obtained the third equation by multiplying both sides of the equation by 2. This eliminates the denominator, 2, from the left side of the equation.
Substitute the obtained value of B in the second given equation to solve for G.
[tex]\begin{gathered} G=2B \\ =2(300) \\ =600 \end{gathered}[/tex]Substitute the obtained value of B into the obtained value of W and then simplify.
[tex]\begin{gathered} W=\frac{1}{2}(3B) \\ =\frac{1}{2}\lbrack3(300)\rbrack \\ =\frac{1}{2}(900) \\ =450 \end{gathered}[/tex]To check if the answer is correct, add all the number of beads per color and determine if the sum is the same as the given value.
[tex]\begin{gathered} G+B+W=1350 \\ 600+300+450=1350 \\ 1350=1350 \end{gathered}[/tex]Since the equation is true, the answers are correct.
Therefore, there must be 600 green beads that were used.
