Hi,but my student in primary school can do algebra already:)

There were some marbles at a shop. The ratio of the number of red marbles to the number of blue marbles was 2:3. When 50 more red marbles and 30 more blue marbles were added, the ratio of the number of red marbles to the number of blue marbles became 5:6. How many marbles were there at first?


x: red marbles
y:blue marbles

x/y=2/3
(x+50)/(y+30)=5/6

Solving the equation,
3x=2y
6x+300=5y+150-----*

if 3x=2y,(here you times 2 for both side right?)
6x=4y

sub into *
4y+300=5y+150
150=y
y=150

if y=150,
use this formula u have found jus now
3x=2y
3x=2(150)=300
after that,bring 3 over,hence 300 /3=100.
x=100

hence red marbles=100
blue marbles=150