Angelique and Serena’s ages are in the ratio 5:3. Serena’s and Venus’ ages are in the ratio 6:5. If
Angelique is 25 years older than Venus, calculate the average age of the three girls.
A = Angelique's ages
S = Serena’s ages
V = Venus’ ages
A / S = 5 / 3
S / V = 6 / 5
Angelique is 25 years older than Venus mean:
A = V + 25
Replace this value in equation:
A / S = 5 / 3
( V + 25 ) / S = 5 / 3 Multiply both sides by S
V + 25 = 5 S / 3 Multiply both sides by 3
3 ( V + 25 ) = 5 S Divide both sides by 5
3 ( V + 25 ) / 5 = S
S = 3 ( V + 25 ) / 5
S / V = 6 / 5 Multiply both sides by V
S = 6 V / 5
S = S
3 ( V + 25 ) / 5 = 6 V / 5 Multiply both sides by 5
3 ( V + 25 ) = 6 V
3 V + 3 * 25 = 6 V
3 V + 75 = 6 V Subtract 3 V to both sides
3 V + 75 - 3 V = 6 V - 3 V
75 = 3 V Divide both sides by 3
75 / 3 = V
25 = V
V = 25
Replace this value in equations:
A = V + 25 and S = 6 V / 5
A = V + 25 = 25 + 25 = 50
S = 6 V / 5 = 6 * 25 / 5 = 150 / 5 = 30
A = 50 , S = 30 , V = 25
average = ( A + S + V ) / 3 =
( 50 + 30 + 25 ) / 3 =
105 / 3 = 35 yrs
Present ageof rose and kate inda ratio 5and 4 three years hence the ages will becom 11and 9.what iskates present age in years
To solve this problem, we'll use a basic understanding of ratios and algebraic equations.
Let's start by assigning variables and writing down the given information:
Let the age of Angelique be A, Serena be S, and Venus be V.
According to the first statement, the ratio of Angelique to Serena's ages is 5:3, which can be written as:
A:S = 5:3
According to the second statement, the ratio of Serena to Venus's ages is 6:5, which can be written as:
S:V = 6:5
Now, we know that Angelique is 25 years older than Venus, which we can express as:
A = V + 25
To find the average age of the three girls, we need to know the sum of their ages. So, let's express the sum of their ages in terms of A, S, and V:
Sum of A + S + V = A + (A - 25) + V
Now, let's solve these equations step by step:
1. From the first statement, we have A:S = 5:3. To make the ratio equal, we can set up the equation:
A/S = 5/3
2. Rearranging the equation from step 1, we get:
A = (5/3)S
3. Using the second statement, we have S:V = 6:5. Again, to make the ratio equal, we can set up the equation:
S/V = 6/5
4. Rearranging the equation from step 3, we get:
S = (6/5)V
5. Substituting the value of S from step 4 into the equation from step 2, we get:
A = (5/3) * (6/5)V
6. Simplifying the equation from step 5, we get:
A = (2/3)V
7. Substituting the value of A from step 6 into the equation A = V + 25, we get:
(2/3)V = V + 25
8. Multiplying both sides of the equation from step 7 by 3 to eliminate the fraction, we get:
2V = 3V + 75
9. Simplifying the equation from step 8, we get:
-V = 75
10. Multiplying both sides of the equation from step 9 by -1, we get:
V = -75
11. Substituting the value of V from step 10 into the equation from step 7, we get:
(2/3) * (-75) = -75 + 25
-50 = -50
Since the equation is true, our calculations are correct.
Now, we can find the values of A and S:
A = (2/3) * (-75) = -50
S = (6/5) * (-75) = -90
Finally, we can calculate the average age of the three girls by finding the sum of their ages and dividing it by 3:
Average age = (A + S + V)/3 = (-50 - 90 - 75)/3 = -215/3 = -71.67 years
Since we can't have a negative age, it is not possible to calculate the average age of the three girls in this scenario.