To find the number, we have to translate first the given mathematical phrases above to an algebraic equation. An algebraic equation is the statement of the equality of two algebraic expressions. Then, an algebraic expression is a combination of constant, variables and algebraic operations.
Constant refers to the known value in an equation and does not change its value.
Variable refers to the symbol or letter, such as "x" or "y" that represents an unknown value.
Equation:
Let "x" be the number.
4 is divided by a number = 4/x
3 divided by the number decreased by 2 = 3/x-2
"4 is divided by a number is equal to 3 divided by the number decreased by 2"
Answers & Comments
Answer:
The number is 8.
Step-by-step explanation:
Finding the Number
To find the number, we have to translate first the given mathematical phrases above to an algebraic equation. An algebraic equation is the statement of the equality of two algebraic expressions. Then, an algebraic expression is a combination of constant, variables and algebraic operations.
Constant refers to the known value in an equation and does not change its value.
Variable refers to the symbol or letter, such as "x" or "y" that represents an unknown value.
Equation:
Let "x" be the number.
4 is divided by a number = 4/x
3 divided by the number decreased by 2 = 3/x-2
"4 is divided by a number is equal to 3 divided by the number decreased by 2"
4 / x = 3 / x-2
Solution:
4 / x = 3 / x-2
4 (x-2) = x (3)
4x - 8 = 3x
4x - 3x = 8
x = 8
Final Answer:
The number is 8.
Checking:
Substitute the number.
4 / x = 3 / x-2
4 / 8 = 3 / 8 - 2
1 / 2 = 3 / 6
1 / 2 = 1 / 2 ✔
Step-by-step explanation: