Honza + Alice + Tonda

Honza + Alice + Tonda have a total of 111 USD. The ratio between Honza and Alena is 5:6, and the ratio between Alice and Tonda is 4:5

How much money has each of them had?

Correct answer:

H =  30
A =  36
T =  45

Step-by-step explanation:


h+a+t = 111
6h = 5a
5a = 4t

h+a+t = 111
6·h = 5·a
5·a = 4·t

a+h+t = 111
5a-6h = 0
5a-4t = 0

Pivot: Row 1 ↔ Row 2
5a-6h = 0
a+h+t = 111
5a-4t = 0

Row 2 - 1/5 · Row 1 → Row 2
5a-6h = 0
2.2h+t = 111
5a-4t = 0

Row 3 - Row 1 → Row 3
5a-6h = 0
2.2h+t = 111
6h-4t = 0

Pivot: Row 2 ↔ Row 3
5a-6h = 0
6h-4t = 0
2.2h+t = 111

Row 3 - 2.2/6 · Row 2 → Row 3
5a-6h = 0
6h-4t = 0
2.467t = 111


t = 111/2.46666667 = 45
h = 0+4t/6 = 0+4 · 45/6 = 30
a = 0+6h/5 = 0+6 · 30/5 = 36

a = 36
h = 30
t = 45

Our linear equations calculator calculates it.



Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Check out our ratio calculator.
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?

You need to know the following knowledge to solve this word math problem:

Related math problems and questions: