Multiple choice general knowledge math & puzzles

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 grandfather now?

  1. 67

  2. 88

  3. 57

  4. 68
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From the previous problem, Miguel is 11 years old. Since M+G=68, the grandfather is 68-11=57 years old. Verification: in 3 years grandfather will be 60, which is 6 times Miguel's age last year (10×6=60). All conditions are satisfied.

AI explanation

To solve this problem, let's assign variables to the ages of Miguel and his grandfather.

Let's say Miguel's present age is M, and his grandfather's present age is G.

According to the problem, in three more years, Miguel's grandfather will be six times as old as Miguel was last year. This can be represented as:

(G + 3) = 6(M - 1)

We also know that when Miguel's present age is added to his grandfather's present age, the total is 68. This can be represented as:

M + G = 68

Now we have a system of two equations with two variables. We can solve this system to find the values of M and G.

Let's first solve the second equation for M:

M = 68 - G

Now substitute this value of M into the first equation:

(G + 3) = 6((68 - G) - 1)

Simplifying the equation:

G + 3 = 6(67 - G)

G + 3 = 402 - 6G

7G = 399

G = 57

Therefore, Miguel's grandfather is currently 57 years old.

The correct answer is C) 57.

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