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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics
1.19 Linear Equations - One Variable

  • An equation is an equality connecting with some unknowns.
  • The unknowns are represented by letters and are called variables.
  • If the equation has only one unknown, it is called an equation with one variable.
  • The word Linear means of degree one.

Example:
Divide 64 into two parts such that three times the greater part will be equal to five times the smaller one.
Solution:
Let x be the greater part. Then 64 - x is the smaller part.
Then 3x = 5(64 - x)
3x = 320 - 5x
3x + 5x = 320
8x = 320
The two parts are 40 and 24.

Example:
Find a number such that one-fourth of it is less than one-third of it by 4.
Solution:
Let the number be x.
One-fourth of it is less than one-third of it by 4: x/4 + 4 = x/3
x/4 + 4 = x/3
x/4 + 4 = x/3
(x+16)/4 = x/3 ---- multiplying both sides by 12 we have
12 ((x+16)/4) = 12 (x/3)
3x + 48 = 4x
3x + 48 - 3x = 4x - 3x
48 = x
The number is 48.


Directions: Solve the following linear equations. Also write at least 10 examples of your own.
Q 1: Divide 25 into two parts so that six times the smaller number is equal to four times the larger number. Find the numbers.
11 and 14
9 and 16
10 and 15

Q 2: Divide 9 into two parts so that thrice the smaller number is equal to twice the larger number plus 2. Find the numbers. (Hint: Let x be the smaller number. Then the larger number is 9-x. The equation can be written as 3(x) = 2 (9-x) + 2. Find x and 9-x)
4 and 5
7 and 5
4 and 6

Q 3: Find a number, if half of which when added to 3, is equal to 12 diminished by 1/4 th of that number. (Hint: Algebraic equation can be written as x/2 + 3 = 12 - x/4 )
10
40
12

Q 4: Divide 17 into two parts so that six times the smaller number is equal to five times the larger number plus 3. Find the numbers.
8 and 9
7 and 10
6 and 11

Q 5: Find a number such that one-third of it is less than one-half of it by four.
26
30
24

Q 6: Dad is seven times as old as his son. 10 years later, he will be three times as old as his son. Find their ages.
dad is 35 years and son is 7 years
dad is 35 years and son is 5 years
dad is 43 years and son is 6 years

Q 7: Find a number such that one-half of it is more than one-third of it by 3.
18
11
12

Q 8: Divide 40 into two parts so that one-third of the greater part may be equal to half of the lesser one.
30 and 10
24 and 16
20 and 10

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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