Question:
Write down equations to solve the following word problems.
Half of a number, plus a fifth of two less than the number ,is four less than the number .What is the number
Answer:
The number is 12
Solution:
Given that,
Half of a number, plus a fifth of two less than the number ,is four less than the number
Let us write the above statement mathematically,
half of number + fifth of two less than the number = four less than number
Let "n" be the number
Therefore,
half of "n" + fifth of two less than "n" = number - 4
[tex]\frac{n}{2} + \frac{1}{5}(n-2) = n-4[/tex]
Simplify the above expression and solve for "n"
[tex]\frac{n}{2} + \frac{n-2}{5} = n - 4\\\\\frac{5n + (n-2)(2)}{2 \times 5} = n-4\\\\[/tex]
[tex]\frac{5n + (n-2)(2)}{10} = n -4\\\\5n + (n-2)(2) = 10n -40\\\\5n + 2n -4=10n-40\\\\7n - 4 = 10n - 40\\\\7n-10n = -40 + 4\\\\-3n = -36\\\\n = \frac{-36}{-3}\\\\n = 12[/tex]
Thus the number is 12
