Miriam is four years older than Ricardo. Ten years ago Miriam was 3 times as old as Ricardo was then.
A: How old are they now?
B: Determine whether your answer is correct by checking that it satisfies the conditions of the problem.
m=r+4
m-10 = 3(r-10)
Miriam is 16 and Ricardo is 12
To solve the problem, let's break it down into steps:
1. Assign variables:
- Let's assign "x" as Ricardo's current age.
- Since Miriam is four years older than Ricardo, her current age can be represented as "x + 4".
2. Set up the equation using the information given:
- Ten years ago, Ricardo's age would have been "x - 10".
- Ten years ago, Miriam's age would have been "(x + 4) - 10".
- According to the problem, Miriam's age ten years ago was three times Ricardo's age then. Therefore, we can set up the equation as:
(x + 4 - 10) = 3(x - 10)
3. Solve the equation:
- Simplify the equation by combining like terms:
x - 6 = 3x - 30
- Subtract "x" on both sides of the equation to isolate the variable:
-6 = 2x - 30
- Add 30 to both sides of the equation to isolate the variable:
24 = 2x
- Divide both sides of the equation by 2 to solve for "x":
x = 12
- Therefore, Ricardo is currently 12 years old.
4. Calculate Miriam's current age:
- Since Miriam is four years older than Ricardo, her current age would be:
x + 4 = 12 + 4
= 16
- Therefore, Miriam is currently 16 years old.
Now let's check if these ages satisfy the conditions of the problem. Ten years ago, Ricardo would have been:
x - 10 = 12 - 10 = 2 years old.
Ten years ago, Miriam would have been:
(x + 4) - 10 = 16 - 10 = 6 years old.
According to the problem, Miriam's age ten years ago was three times Ricardo's age then. In this case:
6 = 3(2)
Since both equations are equal, we can conclude that the ages of Ricardo and Miriam are correct. Ricardo is 12 years old and Miriam is 16 years old.