Question

How much, on average, did the students receive last year if they received 41% less in scholarships and grants this year, with an average of $846 this year? To find out how much the students received on average last year, we need to determine the amount they received this year and then calculate the amount with a 41% reduction. Let Y be the amount received last year. Given this year's average amount is $846 and it's 41% higher than last year, we can write the equation: $846 = Y + 0.41Y Simplify the equation: $846 = 1.41Y Now, solve for Y: Y = $846 / 1.41 ≈ $600 So, on average, the students received approximately $600 last year.

Answer 1

To find the average received last year, divide this year's average ($846) by 0.59, resulting in approximately $1433.90.

Step-by-step explanation:

The question presents a common scenario in mathematics where a percentage decrease needs to be calculated backwards. To find the average amount the students received last year in scholarships and grants, we need to work out the reduced figure provided for this year. Given the average amount received this year is $846 and it represents a 59% value of last year, considering the 41% reduction, we set this up mathematically as follows:

Calculation Steps

1. Denote last year's average amount as Y.
2. Our equation based on the reduction is $846 = Y * 0.59.
3. Solve for Y by dividing the amount received this year by 0.59: Y = $846 / 0.59.
4. Calculate the result: Y ≈ $1433.90.

Therefore, the students received approximately $1433.90 on average last year.