Apply Linear Equations - 8th Grade

​On an algebra test, the lowest grade was 42 points lower than the highest grade. The sum of the two grades was 138. Find the highest grade. 

​You can use a linear equation to solve real-world problems.

​A. What are you asked to find?

​

​

​The highest grade on the algebra test

​B. Assign a variable for the unknown number. Write down what the variable represents.

​Let h be the highest grade.

​C. Write an equation using the information given in the problem.

If ​h is the higest score, then h - 42 is the lowest score.

​

h + (h - 42) = ​138

D. ​Solve the equation.

​h + (h - 42) = 138

​ 2h - 42 = 138

+ 42 + 42

2h = 180

2 2

h = 90

​E. Check the answer.

​h + (h - 42) = 138

​ 90 + (90 - 42) = 138

​ 90 + 48 = 138

138 = 138​

​F. Answer the question in the problem.

​h is the highest grade on the algebra test,

the highest grade on the algebra test was 90.​

​Byron is 2 years older than Steven. Steven is 3 years older than Kent. The sum of the three ages is 26. How old is Kent?

​A. What are you asked to find?

​Kent's age

​B. Assign a variable for the unknown number. Write down what the variable represents.

​

Let x be Kent's age.​

​

​C. Write an equation using the information given in the problem.

​If x is Kent's age, then Steven's age is (x + 3) and Byron's age is ((x + 3) +2).

​

x + ( x + 3 ) + (( x + 3 ) + 2 ) = 26

​D. Solve the equation.

 

​

​

​x + (x + 3) + ((x + 3) + 2) = 26

3x + 8 = 26

​ - 8 - 8

3x = 18 ​

3 3

x = 6

​

​E. Check the answer.

​x + (x + 3) + ((x + 3) + 2) = 26

 6 + (6 + 3) + ((6 + 3) + 2) = 26

6 + 9 + ( 9 + 2 ) ​ = 26

6 + 9 + ​ 11 = 26

26 = 26​

​

​F. Answer the question in the problem.

​

Kent is x, Kent is 6 years old

Multiple Choice

$$2n\ +\ 4\ \ =\ 22$$  

Solve for n.

• n = 13

• n = 9

• n = 36

Multiple Choice

Xander downloads a combination of 27 games and videos. He down loads 5 more videos than games. The equation g + (g + 5) = 27.

How many games did Xander download?

• 11

• 16

• 27

• 32