Four Proportional Numbers

The first number is 50% of the second, the second number is 40% of the third, and the third number is 20% of the fourth. The sum is 396. What are the numbers?

Final Answer:

a =  12
b =  24
c =  60
d =  300

Step-by-step explanation:


a= 50/100 b
b = 40/100 c
c = 20/100 d
a+b+c+d = 396

a= 50/100·b
b = 40/100·c
c = 20/100·d
a+b+c+d = 396

100a-50b = 0
100b-40c = 0
100c-20d = 0
a+b+c+d = 396

Row 4 - 1/100 · Row 1 → Row 4
100a-50b = 0
100b-40c = 0
100c-20d = 0
1.5b+c+d = 396

Row 4 - 1.5/100 · Row 2 → Row 4
100a-50b = 0
100b-40c = 0
100c-20d = 0
1.6c+d = 396

Row 4 - 1.6/100 · Row 3 → Row 4
100a-50b = 0
100b-40c = 0
100c-20d = 0
1.32d = 396


d = 396/1.32 = 300
c = 0+20d/100 = 0+20 · 300/100 = 60
b = 0+40c/100 = 0+40 · 60/100 = 24
a = 0+50b/100 = 0+50 · 24/100 = 12

a = 12
b = 24
c = 60
d = 300

Our linear equations calculator calculates it.



Help us improve the example. If you find a mistake, let us know. Thank you!







Tips for related online calculators
Our percentage calculator will help you quickly and easily solve a variety of common percentage-related problems.
Do you have a linear equation or system of equations and are looking for a 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: