Question

Your cousin renews his apartment lease and pays a new monthly rent. His new rent is calculated by applying a discount of $50 to his original rent and then applying a 10% increase to the discounted amount. What was your cousin's original monthly rent when his new rent is 5% greater?

Your cousin's original rent was $ ________

Answer 1

`\Large \boxed{\sf 1100}`

Explanation:

Let original rent be x

Discount of $50

`x-50`

10% increase

`(x-50) * 1.1`

His new rent is 5% greater than his original rent

`(x-50) * 1.1 = 1.05x`

Solve for x

`x=1100`

Answer 2

• $1100

Explanation:

Let the rent be x

Discounted rent

• x - $50

Increase applied

• 10%

Final rent:

• (x - 50) + 10% = (x - 50)*1.1

We know this is equal to x + 5% = 1.05x, comparing now

• 1.1(x - 50) = 1.05x
• 1.1x - 1.05x = 55
• 0.05x = 55
• x = 55/0.05
• x = $1100