Javier has received scores of 88, 96, 72, and 85 on four of five tests in his history class. His highest score and his final test score will each be weighted 50% more than the other three scores. What score will he have to earn on his final test in order to receive a weighted average score of 88?

To solve this problem, we first need to understand how the weighted average works. The weighted average is calculated by multiplying each value by its corresponding weight, then adding those products together and dividing by the sum of the weights.

1. First, let's calculate the total weight. The highest score and the final test score are each weighted 50% more than the other three scores. So if we assume the weight of the other three scores to be 1, then the weight of the highest score and the final test score would be 1.5 each. So the total weight would be 1*3 (for the three scores) + 1.5 (for the highest score) + 1.5 (for the final test score) = 6.

2. Next, let's calculate the weighted sum of the scores Javier has received so far. His scores are 88, 96, 72, and 85. The highest score is 96, which has a weight of 1.5. The other three scores each have a weight of 1. So the weighted sum would be 881 + 961.5 + 721 + 851 = 88 + 144 + 72 + 85 = 389.

3. Now, we know that Javier wants to receive a weighted average score of 88. The weighted average is calculated by dividing the weighted sum by the total weight. So if we let X be the score Javier needs to earn on his final test, then we have the equation (389 + 1.5X) / 6 = 88.

4. Solving this equation for X gives us X = (88*6 - 389) / 1.5 = 95.4.

So, Javier will need to score approximately 96 on his final test to receive a weighted average score of 88.