Determine Ramiro's Mathematics Weighted Average: Will He Meet the 85 Requirement?

To determine if Ramiro's grades meet the average required, we calculate the weighted average of his grades. This involves applying the formula for calculating a weighted average:

• Multiply each grade by its corresponding weight:
  $92 \times 0.40 = 36.8$
  $78 \times 0.15 = 11.7$
  $98 \times 0.10 = 9.8$
  $83 \times 0.35 = 29.05$
• Sum these products to calculate the weighted average:
  $\text{Weighted Average} = 36.8 + 11.7 + 9.8 + 29.05 = 87.35$

Since 87.35 is greater than the required 85, Ramiro's weighted average meets the high school requirement.

Therefore, the solution to the problem is that Ramiro will be admitted to the high school. His weighted grade average is $87.35$.