Card distribution ratio

The children have 568 cards distributed as follows: Jake and Mike in the ratio of 3:7 and Mike and Larry in the ratio of 3:5. How many cards does Mike have?

Final Answer:

m =  183.5077

Step-by-step explanation:


j+m+l = 568
j = 3/7 · m
m = 3/5 · l

j+l+m = 568
7j-3m = 0
3l-5m = 0

Pivot: Row 1 ↔ Row 2
7j-3m = 0
j+l+m = 568
3l-5m = 0

Row 2 - 1/7 · Row 1 → Row 2
7j-3m = 0
l+1.429m = 568
3l-5m = 0

Pivot: Row 2 ↔ Row 3
7j-3m = 0
3l-5m = 0
l+1.429m = 568

Row 3 - 1/3 · Row 2 → Row 3
7j-3m = 0
3l-5m = 0
3.095m = 568


m = 568/3.0952381 = 183.50769231
l = 0+5m/3 = 0+5 · 183.50769231/3 = 305.84615385
j = 0+3m/7 = 0+3 · 183.50769231/7 = 78.64615385

j = 5112/65 ≈ 78.646154
l = 3976/13 ≈ 305.846154
m = 11928/65 ≈ 183.507692

Our linear equations calculator calculates it.



Help us improve! If you spot a mistake, please let let us know. Thank you!







Tips for related online calculators
Check out our ratio calculator.
Do you have a system of equations and are looking for calculator system of linear equations?

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

algebrabasic operations and conceptsGrade of the word problem

Related math problems and questions: