Question

Barry spent 1/5 of his monthly salary for rent and 1/7 of his monthly salary for his utility bill. If $1012 was left, what was his monthly salary?

Answer 1

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?

Step-by-step 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.

`total\text{ }salary=rent\text{ }payment+utility\text{ }payment+money\text{ }left`

Now Barry uses 1/5 of his salary in rent, that is

`\begin{gathered} rent\text{ }payment=(1)/(5)* his\text{ }total\text{ }salary \\ \\ rent\text{ }payment=(1)/(5)* x \end{gathered}`

Barry uses 1/7 of his salary in utility bill, that is

`\begin{gathered} utility\text{ }bill=(1)/(7)* his\text{ }total\text{ }salary \\ \\ utility\text{ }bill=(1)/(7)* x \end{gathered}`

And after all the payments the money he is left with is 1012 dollars.

`money\text{ }left=1012`

Now let's calculate his total salary

`\begin{gathered} total\text{ }salary=rent\text{ }payment+utility\text{ }bill+money\text{ }left \\ \\ x=(1)/(5)* x+(1)/(7)* x+1012 \\ \\ x=(x)/(5)+(x)/(7)+1012 \\ \\ x=(7x+5x)/(35)+1012 \end{gathered}`

Simplifying it further we get

`\begin{gathered} x=(12x)/(35)+1012 \\ \\ x-(12x)/(35)=1012 \\ \\ (35x-12x)/(35)=1012 \\ \\ (23x)/(35)=1012 \end{gathered}`
`\begin{gathered} 23x=1012*35 \\ \\ 23x=35420 \\ \\ x=(35420)/(23) \\ \\ x=1540 \end{gathered}`

x = 1540 dollars

Final Answer:

Barry's monthly salary is 1540 dollars.