Question

If x and y are positive integers less than 10, and 3x + 2y = 13, using a guess-and check method, what could be the value of y?

Find one of the two possible correct answers. Enter a number for y only!

Hint: Substitute numbers in for x and y and find a pair that works!

y = ____

Answer 1

Explanation:

we can do even a little bit better than wild guessing and trying.

3x + 2y = 13

tells us that the sum of 2 terms is an odd number.

that means one term has to be odd and the other even, as only then their sum will be odd.

2y is because of the included factor 2 an even number. always.

so, 3x has to be odd.

and that means x has to be odd too. because an even number multiplied with any number is always even.

so, x can only be 1 or 3. because 3×5 = 15 (3×7 = 21, 3×9 = 27) and already too big for the sum 13.

so, for x = 1 we have

3×1 + 2y = 13

3 + 2y = 13

2y = 10

y = 5

for x = 3 we have

3×3 + 2y = 13

9 + 2y = 13

2y = 4

y = 2

so, the answer is either y = 2 or y = 5.