Triples

The triplets Jana, Jan, and Judy have saved a total of 180 CZK. Jana has saved three times as much as each of her two siblings. Judy and Jan have saved the same amount.
a) Determine the ratio of the amounts saved by all three siblings in the order Jan, Judy, Jana.
b) Determine the largest amount saved in CZK.

Final Answer:

r = 3:1:1
a =  108 Kc

Step-by-step explanation:

$$\begin{gathered} a+b+c=180 \\ a=3b \\ b=c \\ a=3\cdot b \\ b=c \\ a+b+c=180 \\ a-3b=0 \\ b-c=0 \\ Row2-Row1\to Row2 \\ -4b-c=-180 \\ Row3-\frac{1}{-4}\cdot Row2\to Row3 \\ -1.25c=-45 \\ c=\frac{-45}{-1.25}=36 \\ b=\frac{-180+c}{-4}=\frac{-180+36}{-4}=36 \\ a=180-b-c=180-36-36=108 \\ a=108 \\ b=36 \\ c=36 \\ r=a:b:c=108:36:36 \\ r=3:1:1 \end{gathered}$$

Try another example