To write a variable equation, we need to understand given situation.
The following keys will be helpful to convert the given words as equation.
Sum More than Increased Greater than Plus Added to |
Addition (+) |
Difference Less than decreased fewer than minus subtracted less |
Subtraction (-) |
Product times of |
Multiplication (x) |
divided by quotient |
Division (/) |
Problem 1 :
Let x be the amount of money Ann has. Write an algebraic expression for each of the following
a) Macro has $6 less than Ann has
b) Olivio has 3 times as much money as Ann.
c) Franchesca has $5 more than Ann.
Solution :
a) Here amount that Macro and Ann are having being compared.
Here we see the phrase less than, so we have to use subtraction sign.
Macro has = x - 6
b) 3 times = 3 multiplied by
Olivio has = 3x
c) More than = +
Franchesca has = 5 + x
Problem 2 :
The product of 9 and a number yields 45. Find the number.
A) 6 B) 36 C) 5 D) 405
Solution :
Writing variable equation :
Let x be the unknown number.
The product of 9 and a number = 9x
9x = 45
Solving for x :
To isolate x, we divide by 9 on both sides.
x = 45/9
x = 5
Problem 3 :
The sum of 2, 6, and a number amounts to 15. Find the number.
A) 7 B) 23 C) 19 D) 11
Solution :
Creating variable equation :
Let x be the unknown number.
The sum of 2, 6 and a number = 15
2 + 6 + x = 15
Solving for x :
8 + x = 15
Subtracting by 8 on both sides.
x = 15 - 8
x = 7
So, the required number is 7.
Problem 4 :
The product of a number and -8 gives eight times the sum of that number and 36. Find the number.
A) -18 B) -8 C) 8 D) 18
Solution :
Creating verbal equation :
Let x be the unknown number.
The product of a number and -8 = -8x
eight times the sum of that number and 36 = 8(x + 36)
-8x = 8(x + 36)
Solving for unknown :
Dividing by 8 on both sides.
-x = x + 36
-x - x = 36
-2x = 36
Dividing by -2
x = 36/(-2)
x = -18
Write the sentence as an equation. Use x to represent "a number."
Problem 5 :
Seven subtracted from twice a number gives 17.
A) 2x - 7 = 17 B) 2(x - 7) = 17
C) 7 - 2x = 17 D) 7(2 - x) = 17
Solution :
Creating verbal equation :
Let x be the number.
Twice a number can be represented as 2x
7 subtracted from twice a number, then 2x - 7
So, option A is correct.
Problem 6 :
A number added to -19 is equal to -21.
A) x - 21 = -19 B) -19 + x = -21
C) x = -19 + 21 D) -19 - 21 = x
Solution :
Let x be the unknown number.
x is added to -19, then x + (-19)
That gives -21, then x + (-19) = -21
x - 19 = -21 or (-19) + x = -21
So, option B is correct.
Problem 7 :
Ten subtracted from a number yields 15.
A) 10 + x = 15 B) 10 - x = 15
C) x - 10 = 15 D) 15 - 10 = x
Solution :
Let x be the number.
10 subtracted from a number, then x - 10
That yields = 15, then x - 10 = 15
So, option C is correct.
Problem 8 :
The quotient of 24 and a number is 4.
A) x/24 = 4 B) 24 - x = 4 C) 24/x = 4
D) 24 x = 4
Solution :
Let x be the number.
While dividing 24 and number, we get 4.
24/x = 4, then option C is correct.
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