Two brothers are respectively 5 and 8 years old. In how many years will the ratio of their ages be 4:5
Using Ratios
The trick with ratios is to always multiply or divide the numbers by the same value.
4 : 5 is the same as 4×3 : 5×3 = 12 : 15
Brothers are still three years apart in age.
Ty so muchh
To find out in how many years the ratio of their ages will be 4:5, we need to determine the age difference between the two brothers first.
The age difference is calculated by subtracting the younger brother's age from the older brother's age:
8 - 5 = 3
The ratio of their ages is currently 5:8.
To achieve a ratio of 4:5, we need to reduce the age difference by one unit on both sides of the ratio.
So, we need to find a number of years that will reduce the age difference from 3 to 1.
To do this, we divide the age difference by the difference in the ratio units:
3 / (8 - 5) = 3 / 3 = 1
Therefore, it will take 1 year for the ratio of their ages to be 4:5.
To find in how many years the ratio of their ages will be 4:5, we need to determine the number of years that needs to pass for the younger brother to catch up to the older brother.
Let's assume that it takes x number of years for the younger brother to catch up to the older brother.
At present:
Age of the younger brother = 5 years
Age of the older brother = 8 years
After x number of years:
Age of the younger brother = 5 + x years
Age of the older brother = 8 + x years
According to the problem, the ratio of their ages after x years will be 4:5. Hence, we can write the following equation based on the given information:
(5 + x) / (8 + x) = 4 / 5
Now, let's solve the equation to find the value of x:
Cross-multiplying the equation:
5(5 + x) = 4(8 + x)
25 + 5x = 32 + 4x
Rearranging the terms:
5x - 4x = 32 - 25
x = 7
Therefore, it will take 7 years for the ratio of the two brothers' ages to become 4:5.