Freddy and Frankie want to know their grandmother's age. She tells them that the digits of their age make up her age. She also tells them that their age plus her age total 83. What is the age of the grandmother?
Please explain this question step by step.
It appears that the two boys are less than 10, since adding up all the ages gives only 83
Granny cannot be less than 83-17=66
66+8+9=83
67+7+9=83
68+6+9=68+7+8=83
69+5+9=69+6+8=83
71+5+7=83
72+4+7=72+3+8=72+2+9=83
73+3+7=83 WE HAVE A WINNER!
Thanks Steve
Sure! Let's break down the problem step by step to find the age of the grandmother.
Step 1: Let's assume the grandmother's age has two digits. So, we can represent it as a two-digit number, let's say "AB". Here, A represents the tens digit, and B represents the ones digit.
Step 2: According to the information given, the grandmother tells Freddy and Frankie that the digits of their age make up her age. This means that their age can be represented as "BA".
Step 3: The problem also states that the sum of their ages (Freddy's and Frankie's) plus the grandmother's age totals 83. Mathematically, it can be expressed as:
AB + BA = 83
Step 4: To solve the equation from Step 3, we can rewrite it as:
10A + B + 10B + A = 83
11A + 11B = 83
11(A + B) = 83
Step 5: Since 11 is a prime number and 83 is also a prime number, the only way for the equation to hold true is if A + B equals 7. Therefore, A + B = 7.
Step 6: Now, we can find the possible values of A and B by trying all the combinations that add up to 7. These pairs are (A, B): (1, 6), (2, 5), (3, 4), and (4, 3).
Step 7: However, we need to consider that A and B represent digits of the grandmother's age. This means that A and B should be between 0 and 9. From the possible combinations found in Step 6, only (3, 4) satisfies the condition.
Step 8: Therefore, the grandmother's age, represented by AB, is 34.
So, the grandmother is 34 years old.