Question

A firm needs to rent three temporary offices: a small office, a medium office, and a large office, while their permanent offices are renovated. The rent for the large office is twice as much as the rent for the small office, and the rent for the three offices costs a total of $1,240. The cost of the renovations is $276 and is equal to the sum of 10% of the rent for the small office, 20% of the rent for the medium office, and 30% of the rent for the large office. How much does the rent of each office space cost?

Answer 1

The rent of the small office is $240, the rent of the medium office is $280, and the rent of the large office is $480.

Step-by-step explanation:

Let's assign variables to the rent of each office space:

• Let x be the rent of the small office
• Let y be the rent of the medium office
• Let 2x be the rent of the large office

From the information given, we can set up the following equations:

1. x + y + 2x = 1240 (the total rent for the three offices is $1,240)
2. 0.1x + 0.2y + 0.3(2x) = 276 (the cost of renovations is $276)

Simplifying equation 1, we get:

4x + y = 1240

Substituting 2x for y in equation 2, we get:

0.1x + 0.2(2x) + 0.3(2x) = 276

Now we can solve this system of equations to find the values of x and y:

• Multiplying equation 2 by 10 to eliminate decimals, we get:

x + 4x + 6x = 2760

11x = 2760

x = 2760/11 = 240

Substituting the value of x in equation 1, we get:

4(240) + y = 1240

960 + y = 1240

y = 1240 - 960 = 280

Therefore, the rent of the small office is $240, the rent of the medium office is $280, and the rent of the large office is $480.