Miriam is four years older than Ricardo. 10 years ago she 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 problems
Ricardo ----- x
Miriam ------ x+4
10 years ago:
Ricardo -- x-10
Miriam --- x+4-10 = x-6
at that time she was 3 times as old as Ricardo
x-6 = 3(x-10
x-6 = 3x - 30
-2x = -24
x = 12
Ricardo IS now 12
and Miriam is now 16
You check the answers to make sure the conditions fit.
Let's denote Miriam's current age as M and Ricardo's current age as R.
According to the problem, Miriam is four years older than Ricardo, so we can write the equation: M = R + 4.
Ten years ago, Miriam's age was M - 10, and Ricardo's age was R - 10. At that time, Miriam was three times as old as Ricardo, so we can write the equation: M - 10 = 3(R - 10).
To solve these equations, we can substitute the value of M from the first equation into the second equation.
Substituting M = R + 4 into the second equation, we get:
R + 4 - 10 = 3(R - 10)
Simplifying the equation, we get:
R - 6 = 3R - 30
Combining like terms, we get:
2R = 24
Dividing both sides by 2, we get:
R = 12
Substituting R = 12 back into the first equation, we get:
M = 12 + 4
M = 16
Therefore, Ricardo is currently 12 years old and Miriam is currently 16 years old.
To check if our answer is correct, let's confirm that it satisfies the conditions of the problem:
10 years ago, Ricardo was 12 - 10 = 2 years old, and Miriam was 16 - 10 = 6 years old.
Indeed, 10 years ago, Miriam was 3 times as old as Ricardo.
Therefore, our answer is correct. Ricardo is 12 years old and Miriam is 16 years old.
To solve this problem, we need to set up equations based on the given information.
Let's assume that Ricardo's current age is "x."
According to the information provided, Miriam is four years older than Ricardo. So, Miriam's current age would be "x + 4."
Now, let's consider what happened ten years ago. Ricardo's age at that time would have been "x - 10," and Miriam's age would have been "(x + 4) - 10" or "x - 6."
The problem states that Miriam's age ten years ago was three times Ricardo's age at that time:
x - 6 = 3(x - 10)
Now, let's solve for x:
x - 6 = 3x - 30
Subtract x from both sides:
-6 = 2x - 30
Add 30 to both sides:
24 = 2x
Divide both sides by 2:
x = 12
So, Ricardo's current age (x) is 12 years old. Miriam's current age (x + 4) would be 12 + 4 = 16 years old.
Now, let's check if our solution satisfies the conditions of the problem:
10 years ago, Ricardo's age would have been 12 - 10 = 2, and Miriam's age would have been 16 - 10 = 6. We see that 6 is indeed three times 2, as required by the problem.
Therefore, the answer is:
A) Ricardo is 12 years old, and Miriam is 16 years old.
B) Yes, our answer is correct because it satisfies all the conditions of the problem.