Question

If x,y and z are positive integers such that $27x + 28y + 29z = 363$, find the valve of $(x + y + z)$

Answer 1

Hint: There is no direct formula to find with this value. Use a hit and trial method and get each value closer enough.

Complete step-by-step answer:
Let’s begin with the given equation, which is
$27x + 28y + 29z = 363$
To find the value of x, y and z differently will lead to a greater hurdle of finding the 3 values. Let’s assume all 3 as a single variable k. Then value of K is
$27k + 28k + 29k = 363$
${\text{K}} = 363/84 = 4.32$
So we can Assume that the 3 values remain closer to 4 and at least 1 is greater than 4.
By assuming 2 of them as 4 and one as 5.
i.e., $x = 5,y = 4,z = 4$, we get
$27 \times 5 + 28 \times 4 + 29 \times 4 = 363$. Hence, we get the value we required
Therefore, $x + y + z = 5 + 4 + 4 = 13$

Note: If the number of equations is lesser than the number of variables. Hit and trial is the only option to solve this type of problem.