Respuesta :
Given:
1/5 of Barry's salary was going for his rent.
1/7 of Barry's salary was going for his utility bill.
1012 dollars was left after all the payments.
Required:
What was his monthly salary?
Explanation:
Let us assume that Barry's monthly salary is 'x'
So the sum of his payments and the balance amount will give us his total salary.
[tex]total\text{ }salary=rent\text{ }payment+utility\text{ }payment+money\text{ }left[/tex]Now Barry uses 1/5 of his salary in rent, that is
[tex]\begin{gathered} rent\text{ }payment=\frac{1}{5}\times his\text{ }total\text{ }salary \\ \\ rent\text{ }payment=\frac{1}{5}\times x \end{gathered}[/tex]Barry uses 1/7 of his salary in utility bill, that is
[tex]\begin{gathered} utility\text{ }bill=\frac{1}{7}\times his\text{ }total\text{ }salary \\ \\ utility\text{ }bill=\frac{1}{7}\times x \end{gathered}[/tex]And after all the payments the money he is left with is 1012 dollars.
[tex]money\text{ }left=1012[/tex]Now let's calculate his total salary
[tex]\begin{gathered} total\text{ }salary=rent\text{ }payment+utility\text{ }bill+money\text{ }left \\ \\ x=\frac{1}{5}\times x+\frac{1}{7}\times x+1012 \\ \\ x=\frac{x}{5}+\frac{x}{7}+1012 \\ \\ x=\frac{7x+5x}{35}+1012 \end{gathered}[/tex]Simplifying it further we get
[tex]\begin{gathered} x=\frac{12x}{35}+1012 \\ \\ x-\frac{12x}{35}=1012 \\ \\ \frac{35x-12x}{35}=1012 \\ \\ \frac{23x}{35}=1012 \end{gathered}[/tex][tex]\begin{gathered} 23x=1012\times35 \\ \\ 23x=35420 \\ \\ x=\frac{35420}{23} \\ \\ x=1540 \end{gathered}[/tex]x = 1540 dollars
Final Answer:
Barry's monthly salary is 1540 dollars.
