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Johnny has $12 less than Sarah. Sarah has $35 less than Carla. They have $143. How much money do each of them have?

 Sep 8, 2017
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Johnny has $12 less than Sarah.
Sarah has $35 less than Carla.
They have $143.
How much money do each of them have?

 

Let Johnny = j
Let Sarah = s
Let Carla = c

 

\(\begin{array}{|lrcll|} \hline (1)& s &=& c - 35 \\\\ (2)& j &=& s-12 \quad | \quad s = c-35 \\ & j &=& (c-35) -12 \\ & j &=& c - 47 \\\\ (3)& j+s+c &=& 143 \quad | \quad j = c - 47 \qquad s = c-35 \\ & (c-47)+(c-35)+c &=& 143 \\ & 3c -47 -35 &=& 143 \\ & 3c &=& 143 + 47 + 35 \\ & 3c &=& 225 \quad | \quad : 3 \\ & \mathbf{c} & \mathbf{=}& \mathbf{75} \\\\ & j &=& c-47 \quad | \quad c = 75 \\ & j &=& 75-47 \\ & \mathbf{j} & \mathbf{=}& \mathbf{28} \\\\ & s &=& c - 35 \quad | \quad c = 75 \\ & s &=& 75 - 35 \\ & \mathbf{s} & \mathbf{=}& \mathbf{40} \\\\ \hline \end{array}\)

 

\(\begin{array}{lr} \text{Johnny} & $28 \\ \text{Sarah} & $40 \\ \text{Carla} & $75 \\ \end{array}\)

 

laugh

 Sep 8, 2017
edited by heureka  Sep 8, 2017

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