Answer:
3x + 2y = 34. and two possible pairs of positive numbers are (x, y) = (10, 2) and (x, y) = (4, 11).
Step-by-step explanation:
Let the First positive number be x and second positive number be y.
Triple of first number = 3x
double of second number = 2y
According to question,
3x + 2y = 34
Therefore, the equation is 3x + 2y = 34
So the two possible pair of numbers Diego would be thinking of must satisfy the equation 3x + 2y = 34
Now, 3x + 2y = 34
3x = 34 - 2y
Let x = 10 and by substituting its value in above expression,
[tex]3 \times 10 = 34 - 2y[/tex]
[tex]30 = 34 - 2y[/tex]
[tex]2y = 34 - 30[/tex]
[tex]2y = 4[/tex]
[tex]y = 2[/tex]
Therefore first pair (x, y) = (10, 2)
In the same way put x = 4 then,
3x = 34 - 2y
[tex]3 \times 4 = 34 - 2y[/tex]
[tex]2y = 34 - 12[/tex]
[tex]2y = 22[/tex]
[tex]y = 11[/tex]
Therefore first pair (x, y) = (4, 11)
Therefore, (x, y) = (4, 11) and (x, y) = (10, 2) are the two possible pairs of numbers Diego could be thinking of as these both values satisfy the equation 3x + 2y = 34.
