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On an algebra test, the highest grade was 50 points higher than the lowest grade. The sum of the two grades was 122. Find the lowest grade.

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Answer:

Low Score: 36

High Score: 86

Step-by-step explanation:

We can represent the highest and lowest grades with the variables:

[tex]H[/tex] and [tex]L[/tex].

In equation form, we can write out the given information:

  • "the highest grade was 50 points higher than the lowest grade"
    ⇒   [tex]H = L + 50[/tex]
  • "the sum of the two grades was 122"
    ⇒   [tex]H+L=122[/tex]

We now have a system of equations, which we can solve by substitution. We are given a definition for H in terms of L. Substituting this in for H in the second equation, we get:

[tex](L+50) + L = 122[/tex]

↓ combining like terms

[tex]2L + 50 = 122[/tex]

↓ subtracting 50 from both sides

[tex]2L = 72[/tex]

↓ dividing both sides by 2

[tex]\boxed{L = 36}[/tex]

So, the low score was 36. We can now solve for the high score by plugging the low score into the first equation:

[tex]H = L + 50[/tex]

[tex]H = 36 + 50[/tex]

[tex]\boxed{H = 86}[/tex]

So, the high score was 86.

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