Question

1. on an algebra test, the highest grade was 56 points more than the lowest grade. (in statistics, the difference between the largest number and the smallest number is known as the range.) the sum of the two grades was 128. what were the highest and lowest grades on the test?

Explanation:

Step1: Let variables

Let the lowest grade be $x$. Then the highest grade is $x + 56$.

Step2: Set up equation

Since the sum of the two grades is 128, we have the equation $x+(x + 56)=128$.

Step3: Simplify the equation

Combine like - terms: $2x+56 = 128$.

Step4: Solve for $x$

Subtract 56 from both sides: $2x=128 - 56$, so $2x = 72$. Then divide both sides by 2: $x=\frac{72}{2}=36$.

Step5: Find the highest grade

The highest grade is $x + 56$. Substitute $x = 36$ into it, we get $36+56 = 92$.

Answer:

The lowest grade is 36 and the highest grade is 92.