1. The problem is to simplify the expression $$4.2a + 3b - 0.5a$$ and find the coefficient of $$a$$ in the simplified form. 2. To simplify, combine like terms. Like terms are terms that have the same variable raised to the same power. 3. Here, $$4.2a$$ and $$-0.5a$$ are like terms because both have the variable $$a$$. 4. Add their coefficients: $$4.2 - 0.5 = 3.7$$. 5. So, $$4.2a - 0.5a = 3.7a$$. 6. The term $$3b$$ has no like terms to combine with, so it remains as is. 7. The simplified expression is $$3.7a + 3b$$. 8. Therefore, the number that goes in the green box (coefficient of $$a$$) is $$3.7$$. 9. The number that goes in the grey box (coefficient of $$b$$) is $$3$$ (given, no change).