The ratio of ali's age to ben's age is 21: 17.if the difference in ages between them is 3 years and 4 months, find ali's age, in years and months.

To find the answer from the question above, we need to solve the equation and find Ali's age. We know that the ratio of Ali's age and Ben's age is 21:17 and they have age's difference in 3 years and 4 months. We need to find how many years old is Ali in years and months.

First, we made an equation with the ration which has known

21/(21 +17) = 21/38x = Ali's age

17/(21+17) = 17/38x = Ben's age

Ali's age - Ben's age = 3 years 4 month

           21/38 - 17/38 = 4/38x = 3 years 4 month

and we use x as a symbol for the total of Ali's age and Ben's age

to make it easier, we change the unit of the time. from year to month

3 years + 4 months = (3 x 12 months) + 4 months = 40 months

we need to know what is the value of x, we can finish a first equation which is the age's difference

4/38x = 40 months

          x = 40/4 x 38

          x = 10 x 38 = 380 months

because we know the value of x is 380, now we can finish the other equation

Ali's age

          21/38x = 21/38 x 380 = 21 x 10 = 210 months

          * if we would know how many years old Ali in years and months then we change the unit, 1 year = 12 months so, 210 divided by 12 is 17 and 6 left. So Ali's age is 17 years and 6 months.

Ben's age

          17/38x = 17/38 x 380 = 17 x 10 = 170 months

         * we change the unit to year, so if 170 divided by 12 is 14 and 2 left.       So, Ben's age is 14 years and 2 months

Learn More :

The ratio of Paul’s age to Luis’s age is 2:3. The sum of their ages is 35 years. Find the age of each one.

2. The ratio of zoya's age to nelya's age is 1:4. twenty years from now, nelya will be twice as old as zoya will be then. find their present ages

3. Sean’s age and Helen’s age are in the ratio of 3:5. Two years ago, Helen was twice as old as Sean was then. Find their present ages.

Answer Details

Subject: Mathematics

Chapter: Fraction

Grade: Middle School

Keywords : The average age of Ali, Ben and Chandra, Vic and Ben ages are in the ratio of 3 : 4, The ratio of Paul's age to Luis's age is 2 : 3

use substitution to solve each system of equations. y = x + 5 3x + y = 25 62/87,21 y = x + 5 3x + y = 25 substitute x + 5 for y in the second equation. substitute the solution for x into either equation to find y. the solution is (5, 10)

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