Question

The ages of Benita and Ben are in the ratio of 5:7. Four years from now, the ratio of their ages will be 3:4. Find their ages.

a) Benita: 15, Ben: 21
b) Benita: 20, Ben: 28
c) Benita: 25, Ben: 35
d) Benita: 30, Ben: 42

Answer 1

Benita's age is 20 and Ben's age is 28.

Step-by-step explanation:

To solve this problem, we can set up two equations using the given information. Let's say the ages of Benita and Ben currently are 5x and 7x, respectively. Four years from now, their ages will be (5x + 4) and (7x + 4). According to the second ratio given, we can write the equation: (5x + 4) / (7x + 4) = 3 / 4.

To solve this equation, we can cross-multiply:

• 4(5x + 4) = 3(7x + 4)
• 20x + 16 = 21x + 12
• x = 4

Now that we have found the value of x, we can substitute it back into the original ratios to find the ages of Benita and Ben: Benita's age is 5x = 5(4) = 20, and Ben's age is 7x = 7(4) = 28.