Question

Elizabeth writes down: One multiple of 13; and Two different factors of 77. Elizabeth adds up her three numbers. Her answer is greater than fifty but less than sixty. What three numbers could Elizabeth have written down?​

Answer 1

Answer:

7, 11, 39 OR -26, 1, 77;

Step-by-step explanation:

Mumble. Let's call the first number 13k, which is obviously a multiple of 13.

The factor of 77 are easy to find. It's either 77 and 1, or 11 and 7.

Now two cases. If we consider negative multiples of 13 (ie, -39 is -3 times 13) we can use the first pair (77 and 1, who sum up to 78, and start taking 13 from it as many times as we need to get to our interval.

1st pass: 78-13 = 65 out

2nd pass: 65-13 = 52 in

3rd pass : 52 - 13 = 39 out

So a possible triplet is 77, 1 and -26.

Case two: we aren't allowed to take negative numbers, and 77 and 1 will bring out of our range already. Let's stick to 11 and 7, who sum up to 18. Again, let's keep adding 13 as many times as we need

1st pass: 18+13 = 31, no good

2nd pass: 31+13 = 44, out again

3rd pass: 44+13= 57, we're good!

4th pass: 57+13 = 70, too far.

So another possible triplet is 7, 11, 39.

The moment you allow the product of the second and third number to be rationals will open a whole new can of worm that isn't any close to be interesting or fun to explore.