+26367 Hey guys I'm Kendall pls help me with this question : in a box 1/4 of the buttons are red. There are 32 more yellow buttons than red buttons. The remaining 86 buttons are blue. How many buttons are there in the box altogether?
\(\begin{array}{rcll} \text{red} &=& \frac{ \text{box} } {4} \\\\ \text{yellow} &=& 32 + \text{red} \\ &=& 32 + \frac{ \text{box} } {4} \\\\ \text{blue} &=& 86 \\ \\ \hline \\ \text{box} &=& \text{red} ~+ ~\text{yellow} ~ + ~\text{blue}\\ \text{box} &=& \frac{ \text{box} } {4} ~+ ~32 + \frac{ \text{box} } {4} ~ + 86\\ \text{box} &=& 2\cdot \frac{ \text{box} } {4} ~+ 32 + 86\\ \text{box} &=& 2\cdot \frac{ \text{box} } {4} ~+ 118\\ \text{box} &=& \frac{ \text{box} } {2} ~+ 118 \qquad | \qquad \cdot 2\\ 2\cdot \text{box} &=& \text{box} ~+ 118\cdot 2 \\ 2\cdot \text{box} &=& \text{box} ~+ 236 \qquad | \qquad -\text{box}\\ 2\cdot \text{box}-\text{box} &=& 236 \\ \text{box} &=& 236 \\ \end{array}\)
There are 236 buttons in the box
\(\begin{array}{rcll} \text{red} &=& \frac{236}{4} \\ &=& 59 \\\\ \text{yellow} &=& 32+59 \\ &=& 91 \\\\ \text{blue} &=& 86 \\\\ 59+91+86 &=& 236 \end{array}\)
+33615 buttons (b) = red (1/4b) + yellow(1/4b +32) + blue(86)
b = (1/4)b + (1/4)b+ 32 + 86
b = (1/2)b + 118
(1/2)b = 118
b = 236
+26367 Hey guys I'm Kendall pls help me with this question : in a box 1/4 of the buttons are red. There are 32 more yellow buttons than red buttons. The remaining 86 buttons are blue. How many buttons are there in the box altogether?
\(\begin{array}{rcll} \text{red} &=& \frac{ \text{box} } {4} \\\\ \text{yellow} &=& 32 + \text{red} \\ &=& 32 + \frac{ \text{box} } {4} \\\\ \text{blue} &=& 86 \\ \\ \hline \\ \text{box} &=& \text{red} ~+ ~\text{yellow} ~ + ~\text{blue}\\ \text{box} &=& \frac{ \text{box} } {4} ~+ ~32 + \frac{ \text{box} } {4} ~ + 86\\ \text{box} &=& 2\cdot \frac{ \text{box} } {4} ~+ 32 + 86\\ \text{box} &=& 2\cdot \frac{ \text{box} } {4} ~+ 118\\ \text{box} &=& \frac{ \text{box} } {2} ~+ 118 \qquad | \qquad \cdot 2\\ 2\cdot \text{box} &=& \text{box} ~+ 118\cdot 2 \\ 2\cdot \text{box} &=& \text{box} ~+ 236 \qquad | \qquad -\text{box}\\ 2\cdot \text{box}-\text{box} &=& 236 \\ \text{box} &=& 236 \\ \end{array}\)
There are 236 buttons in the box
\(\begin{array}{rcll} \text{red} &=& \frac{236}{4} \\ &=& 59 \\\\ \text{yellow} &=& 32+59 \\ &=& 91 \\\\ \text{blue} &=& 86 \\\\ 59+91+86 &=& 236 \end{array}\)
