Question5Max. score: 4.00Alice and Tara's present age is in the ratio of 13:5 respectively. After 4 years, the ratio of their ages will become 7:3 respectively. What is Alice's present age?4 years old20 years old52 years old55 years old
Question
Question5Max. score: 4.00Alice and Tara's present age is in the ratio of 13:5 respectively. After 4 years, the ratio of their ages will become 7:3 respectively. What is Alice's present age?4 years old20 years old52 years old55 years old
Solution
To solve this problem, we can set up a system of equations based on the given information.
Let's assume Alice's present age is 13x and Tara's present age is 5x, where x is a constant.
According to the problem, after 4 years, Alice's age will be 13x + 4 and Tara's age will be 5x + 4.
The ratio of their ages after 4 years is given as 7:3, so we can write the equation:
(13x + 4) / (5x + 4) = 7/3
To solve this equation, we can cross-multiply:
3(13x + 4) = 7(5x + 4)
Simplifying the equation, we get:
39x + 12 = 35x + 28
Subtracting 35x from both sides, we have:
4x + 12 = 28
Subtracting 12 from both sides, we get:
4x = 16
Dividing both sides by 4, we find:
x = 4
Now, we can find Alice's present age by substituting x = 4 into the expression 13x:
Alice's present age = 13 * 4 = 52 years old
Therefore, Alice's present age is 52 years old.
Similar Questions
Alice and Tara's present age is in the ratio of 13:5 respectively. After 4 years, the ratio of their ages will become 7:3 respectively. What is Alice's present age?4 years old20 years old52 years old55 years old
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