I need help in solving this word problem using linear system equation...I.m not sure how to start,,,

A hotel rents a double occupanch room for $20 more than a single occupancy room. One night, the hotel took in $3115 after renting 15 double occupancy rooms and 26 single occupancy room. I need to write and solve a linear system equatio to find the cost of renting a double occupancy room and the cost of renting a single occupancy room...I don't know where to start...please help I'm confused.



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To solve this word problem using a linear system of equations, we need to define two variables:

Let's say the cost of renting a double occupancy room is x dollars.
And let's say the cost of renting a single occupancy room is y dollars.

Now, let's set up the equations:

1. The hotel rents 15 double occupancy rooms, so the total cost for these rooms would be 15x dollars.
2. The hotel also rents 26 single occupancy rooms, so the total cost for these rooms would be 26y dollars.
3. The hotel took in a total of $3115, so the sum of the costs of the double occupancy rooms and the single occupancy rooms should be equal to that: 15x + 26y = 3115.

Now, we have a system of equations:

Equation 1: 15x + 26y = 3115

To solve this system of equations, you can use the method of substitution or elimination.

Let's use the method of substitution:

1- Solve equation 1 for one of the variables. Let's solve it for x:
15x = 3115 - 26y
x = (3115 - 26y)/15

Now, you can substitute this expression for x into equation 2 to solve for y.

Once you find the value of y, you can substitute it back into the equation x = (3115 - 26y)/15 to find the value of x.

This will give you the cost of renting a double occupancy room (x) and the cost of renting a single occupancy room (y).

let rental of single room be x dollars,

then rent for double room is x+20

15x + 26(x+20) = 3115

I leave it up to you to solve that simple equation.