Let the numbers that Diego thinks are x and y.
It is given that the sum of twice the first number and thrice the second number is 102.
Therefore, 2x + 3y = 102.
2x = 102 - 3y
[tex]x=51-\frac{3}{2} y[/tex]
To get the integral solution for x, the smallest number we can substitute for y is 2.
So,
[tex]x=51-\frac{3}{2} (2)[/tex]
x = 51 - 3
x = 48
Hence, the numbers that Diego thinks are 48 and 2.
Check:
2(48) + 3(2) = 96 + 6 = 102
