The highest score on an algebra test is 42 points more than the lowest. when added together, the lowest and highest score was 154. find both the lowest and highest score.

Question

The highest score on an algebra test is 42 points more than the lowest. when added together, the lowest and highest score was 154. find both the lowest and highest score.

Answer 1

For this problem, we have two unknown quantities. The first being the highest score and the second being the lowest score. Let’s choose a variable to represent each of these:

x = highest score

y = lowest score

Now, using these variables, we will write math equations that model the information given in the problem.

”The highest text score is 42 points more than the lowest” becomes x = 42 + y

”When added together, the lowest and highest score was 154” becomes x +y = 154.

Now that we have two equations, we will be able to solve for the two unknowns, x and y.

Then first equation tells us that x is equal to “42+y”. Since this is what x is equal to, we can replace the x in the second equation with “42+y” to get:

(42+y) +y =154

Now, collecting the like terms, y +y become 2y:

42 +2y = 154

Subtracting 42 from both sides yields:

2y = 112

Lastly, dividing by 2 on both sides:

y=56.

We can now plug 56 in for y in either of the two original equations. I will choose the first equation, x=42+y

x = 42 + (56)

x=98.

So, the highest test score was 98, and the lowest test score was 56.