CZK coins

Thaddeus and Jolana together have 15 CZK. Jolana has half of Thaddeus' money. Nevertheless, Jolana has three coins and Thaddeus 2 coins. Which coin has Thaddeus and Jolana (Help: CZK coins have values 1,2,5,10,20,50 CZK)?

Correct answer:

t =  10 Kč
j =  5 Kč

Step-by-step explanation:

$$\begin{gathered} t+j=15 \\ j=t/2 \\ t=10Kc=5+5Kc \\ s=5Kc=2+2+1Kc \end{gathered}$$

t+j = 15
j = 1/2 · t

j+t = 15
2j-t = 0

Pivot: Row 1 ↔ Row 2
2j-t = 0
j+t = 15

Row 2 - 1/2 · Row 1 → Row 2
2j-t = 0
1.5t = 15


t = 15/1.5 = 10
j = 0+t/2 = 0+10/2 = 5

j = 5
t = 10

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