1.
In three more years, Miguel's grandfather will be six times as old as Miguel was last year. When Miguel's present age is added to his grandfather's present age, the total is 68. How old is each one now?
Correct Answer
A. The grandfather is 57 years old
Miguel is presently 11 years old
Explanation
In three more years, Miguel's grandfather will be six times as old as Miguel was last year. This means that the grandfather's age in three years will be six times Miguel's age last year. Let's assume Miguel's age last year was x. So, in three years, the grandfather's age will be 6x.
Now, let's consider the present ages. We know that the sum of Miguel's and his grandfather's present ages is 68. Let's assume Miguel's present age is y. So, the grandfather's present age will be 68 - y.
From the given information, we can set up the equation: 6x = 68 - y.
Since Miguel's present age is 11, we can substitute y = 11 into the equation: 6x = 68 - 11.
Simplifying this equation, we get 6x = 57. Solving for x, we find that x = 9.
Therefore, Miguel's age last year was 9, and his grandfather's present age is 57.
2.
One-half of Heather's age two years from now plus one-third of her age three years ago is twenty years. How old is she now?
Correct Answer
D. Heather is 24 years old.
Explanation
Let's assume Heather's current age is x. Two years from now, her age will be x + 2. Three years ago, her age was x - 3. According to the given information, (1/2)(x + 2) + (1/3)(x - 3) = 20. Simplifying this equation, we get (3x + 6 + 2x - 6)/6 = 20. Combining like terms, we have 5x/6 = 20. Multiplying both sides by 6/5, we find x = 24. Therefore, Heather is currently 24 years old.
3.
John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, John will be three times as old as Alice. How old is Peter now?
Correct Answer
A. Peter is now 10 years old.
Explanation
John is currently twice as old as Peter.
Peter is 5 years older than Alice, meaning if you take Peter's age and subtract 5 years, you get Alice's current age.
In 5 years, John will be three times as old as Alice is now. Since we know John's future age relation to Alice's current age, we can set up a relationship between their ages to solve the problem.
To find Peter's current age, we use the information that in 5 years, the difference in age between John and Alice, considering John's age as twice Peter's, reveals Peter's age relation to Alice. Knowing Peter is 5 years older than Alice and applying the condition about John's age in 5 years being three times Alice's current age allows us to calculate Peter's age. Through a series of substitutions and simplifications based on these relationships, we find that Peter is 10 years old now.
4.
The sum of Ben and carol's age is 36. Nine years ago, Ben was twice as old as Carol. How old is each now?
Correct Answer
C. Ben's age now is 21,
Carol's age now is 15.
Explanation
Let's assume Ben's age is B and Carol's age is C. According to the given information, B + C = 36. Nine years ago, Ben's age was B - 9 and Carol's age was C - 9. It is also stated that Ben was twice as old as Carol at that time, so we can write the equation B - 9 = 2(C - 9). Solving these two equations simultaneously, we get B = 21 and C = 15. Therefore, Ben's age now is 21 and Carol's age now is 15.
5.
Sam is 3 years younger than Alex and Alex is 7 years older than Mary. If the sum of their ages is 44, find each persons age.
Correct Answer
D. Alex's age = 18 Sam's age = 15 Mary's age = 11
Explanation
Let's assume Sam's age as x. Since Sam is 3 years younger than Alex, Alex's age would be x + 3. Since Alex is 7 years older than Mary, Mary's age would be x - 4. The sum of their ages is given as 44, so we can form the equation x + (x + 3) + (x - 4) = 44. Solving this equation, we get x = 15. Therefore, Sam's age is 15, Alex's age is 18, and Mary's age is 11.
6.
Miguel is 46 years old. He is 4 years older than thrice his Niko's age. Find the age of Niko.
Correct Answer
B. Niko is 14 years old.
Explanation
The question states that Miguel is 46 years old and is 4 years older than thrice Niko's age. Let's assume Niko's age to be x. According to the given information, Miguel's age can be expressed as 3x + 4. We are told that Miguel is 46 years old, so we can set up the equation 3x + 4 = 46. Solving this equation, we find that x = 14. Therefore, Niko is 14 years old.
7.
Edward, Bryan and Mark are cousins.Edawrdâ€™s age is one-third of Bryan and Mark is five years elder than Bryan. If the sum of the age of the cousins is 40, find the ages of each.
Correct Answer
A. Edward=5
Bryan=15
Mark=20
Explanation
Edward's age is one-third of Bryan's age, so if Bryan is 15 years old, Edward would be 5 years old. Mark is five years older than Bryan, so if Bryan is 15 years old, Mark would be 20 years old. The sum of their ages is 5 + 15 + 20 = 40, which matches the given information. Therefore, the ages of Edward, Bryan, and Mark are 5, 15, and 20 respectively.