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I have a bag with red and green marbles in it. At the moment, the ratio of red marbles to green marbles is 3:2. If I add 5 red marbles and 5 green marbles, the ratio will be 4:3. How many red marbles will be in the bag after I add more?

Jun 19, 2021

#1
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I have a bag with red and green marbles in it.
At the moment, the ratio of red marbles to green marbles is 3:2.
If I add 5 red marbles and 5 green marbles, the ratio will be 4:3.
How many red marbles will be in the bag after I add more?

$$\begin{array}{|lrcll|} \hline (1)& \dfrac{r}{g} &=& \dfrac{3}{2} \\\\ & \mathbf{r} &=& \mathbf{\dfrac{3}{2}g} \\ \hline (2)& \dfrac{r+5}{g+5} &=& \dfrac{4}{3} \\\\ & r+5 &=& \dfrac{4}{3}(g+5) \\\\ & \dfrac{3}{2}g +5 &=& \dfrac{4}{3}(g+5) \\\\ & \dfrac{3}{2}g-\dfrac{4}{3}g &=& \dfrac{20}{3}-5 \\\\ & g\left(\dfrac{3}{2}-\dfrac{4}{3}\right) &=& \dfrac{5}{3} \\\\ & g\left(\dfrac{1}{6}\right) &=& \dfrac{5}{3} \\\\ & g &=& \dfrac{5}{3}* 6 \\\\ & \mathbf{g} &=& \mathbf{10} \\ \hline & \mathbf{r} &=& \mathbf{\dfrac{3}{2}g} \\ & r &=& \dfrac{3}{2}*10 \\ & \mathbf{r} &=& \mathbf{15} \\ & \mathbf{r+5} &=& \mathbf{20} \\ \hline \end{array}$$ Jun 19, 2021