There were 5 times as many cans of green tea as cans of orange juice in a shop. After 24 cans of orange juice were sold, the number of cans of green tea was 25 times the number of cans of orange juice. How many cans of green tea and orange juice were there altogether at first?

Answer 1

Let's say the number of cans of orange juice was x.
The number of cans of green tea was 5*x.
When 24 cans of orange juice were sold, the number of green tea cans was 25*(x-24).
Since there were 5 times as many cans of green tea as cans of orange juice in a shop, the equation that represents this is 5*x=25*(x-24).
Multiplying through the brackets gives 5*x=25*x-25*24.
When you take 25*24 to the right side and subtract 25 times the difference between x and 24 from 25*x you get 25*x-5*x=25*24.
The left side of the equation becomes 20*x=25*24.
Dividing both sides by 20 gives x= 25*24/20
x=30
At first, the number of cans of green tea was 30*5 = <<30*5=150>>150.
Altogether, there were 150+30 = <<150+30=180>>180 cans of green tea and orange juice. Answer: \boxed{180}.