Honza + Alice + Tonda

Honza + Alice + Tonda have a total of 1036 USD. The ratio between Honza and Alena is 5:6, and the ratio between Alice and Tonda is 4:5

How much money does each of them have?

Final Answer:

h =  280
a =  336
t =  420

Step-by-step explanation:

$$\begin{gathered} h:a=5:6 \\ a:t=4:5 \\ h+a+t=1036 \\ 6h=5a \\ 5a=4t=6h \\ h+\frac{6}{5}h+\frac{6}{4}\cdot h=1036 \\ h+6/5\cdot h+6/4\cdot h=1036 \\ 74h=20720 \\ h=\frac{20720}{74}=280 \\ h=280 \end{gathered}$$

$a=\frac{6}{5}\cdot h=\frac{6}{5}\cdot 280=\frac{6\cdot 280}{5}=\frac{1680}{5}=336$

$$\begin{gathered} t=\frac{6}{4}\cdot h=\frac{6}{4}\cdot 280=\frac{6\cdot 280}{4}=\frac{1680}{4}=420 \\ \text{ Verifying Solution: } \\ {s}_2=h+a+t=280+336+420=1036\text{eur} \\ {r}_1=h:a=280:336=\frac{5}{6}\doteq 0.8333=5:6 \\ {r}_2=a:t=336:420=\frac{4}{5}=0.8=4:5 \end{gathered}$$

Try another example