Euros

Peter, Jane, and Thomas have € 550 together. Tomas has 20 euros more than Jane, and Peter € 150 less than Thomas. Determine how much each of them has.

Final Answer:

P =  90
J =  220
T =  240

Step-by-step explanation:

$$\begin{gathered} P+J+T=550 \\ T=20+J \\ P=T-150 \\ J+P+T=550 \\ J-T=-20 \\ P-T=-150 \\ Row2-Row1\to Row2 \\ J+P+T=550 \\ -P-2T=-570 \\ P-T=-150 \\ Row3+Row2\to Row3 \\ J+P+T=550 \\ -P-2T=-570 \\ -3T=-720 \\ T=\frac{-720}{-3}=240 \\ P=\frac{-570+2T}{-1}=\frac{-570+2\cdot 240}{-1}=90 \\ J=550-P-T=550-90-240=220 \\ J=220 \\ P=90 \\ T=240 \end{gathered}$$

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