Math / Algebra

QuestionQuestion 9 of 10 This question: 5 point(s) possible
Benjamin \& Associates, a real estate developer, recently built 205 condominiums in McCall, Idaho. The condos were either three-bedroom units or four-bedroom units. If the total number of bedrooms in the entire complex is 732 , how many three-bedroom units are there? How many four-bedroom units are there?
There are $\square$ three-bedroom units and $\square$ four-bedroom units.

Studdy Solution

STEP 1

1. There are a total of 205 condominiums.
2. Each condominium is either a three-bedroom unit or a four-bedroom unit.
3. The total number of bedrooms in all the condominiums is 732.
4. We need to find the number of three-bedroom units and four-bedroom units.

STEP 2

1. Define variables for the number of three-bedroom and four-bedroom units.
2. Set up a system of equations based on the given information.
3. Solve the system of equations.

STEP 3

Define variables for the number of three-bedroom and four-bedroom units.
Let $x$ be the number of three-bedroom units and $y$ be the number of four-bedroom units.

STEP 4

Set up a system of equations based on the given information.
Equation 1: The total number of units is 205. $x + y = 205$
Equation 2: The total number of bedrooms is 732. $3x + 4y = 732$

STEP 5

Solve the system of equations.
First, solve Equation 1 for $y$ : $y = 205 - x$
Substitute $y = 205 - x$ into Equation 2: $3x + 4(205 - x) = 732$
Simplify and solve for $x$ : $3x + 820 - 4x = 732$ $-x + 820 = 732$
Subtract 820 from both sides: $-x = 732 - 820$ $-x = -88$
Multiply both sides by -1: $x = 88$

STEP 6

Now, substitute $x = 88$ back into the equation for $y$ : $y = 205 - 88$ $y = 117$
So, there are $\boxed{88}$ three-bedroom units and $\boxed{117}$ four-bedroom units.

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Studdy Solution

STEP 1

1. There are a total of 205 condominiums.
2. Each condominium is either a three-bedroom unit or a four-bedroom unit.
3. The total number of bedrooms in all the condominiums is 732.
4. We need to find the number of three-bedroom units and four-bedroom units.

STEP 2

1. Define variables for the number of three-bedroom and four-bedroom units.
2. Set up a system of equations based on the given information.
3. Solve the system of equations.

STEP 3

Define variables for the number of three-bedroom and four-bedroom units.
Let $x$ be the number of three-bedroom units and $y$ be the number of four-bedroom units.

STEP 4

Set up a system of equations based on the given information.
Equation 1: The total number of units is 205. $x + y = 205$
Equation 2: The total number of bedrooms is 732. $3x + 4y = 732$

STEP 5

STEP 6

Now, substitute $x = 88$ back into the equation for $y$ : $y = 205 - 88$ $y = 117$
So, there are $\boxed{88}$ three-bedroom units and $\boxed{117}$ four-bedroom units.

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Studdy Solution

STEP 1

1. There are a total of 205 condominiums.2. Each condominium is either a three-bedroom unit or a four-bedroom unit.3. The total number of bedrooms in all the condominiums is 732.4. We need to find the number of three-bedroom units and four-bedroom units.

STEP 2

1. Define variables for the number of three-bedroom and four-bedroom units.2. Set up a system of equations based on the given information.3. Solve the system of equations.

STEP 3

Define variables for the number of three-bedroom and four-bedroom units.Let x x x be the number of three-bedroom units and y y y be the number of four-bedroom units.

STEP 4

Set up a system of equations based on the given information.Equation 1: The total number of units is 205. x+y=205 x + y = 205 x+y=205Equation 2: The total number of bedrooms is 732. 3x+4y=732 3x + 4y = 732 3x+4y=732

STEP 5

STEP 6

Now, substitute x=88 x = 88 x=88 back into the equation for y y y: y=205−88 y = 205 - 88 y=205−88 y=117 y = 117 y=117So, there are 88 \boxed{88} 88​ three-bedroom units and 117 \boxed{117} 117​ four-bedroom units.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. There are a total of 205 condominiums.
2. Each condominium is either a three-bedroom unit or a four-bedroom unit.
3. The total number of bedrooms in all the condominiums is 732.
4. We need to find the number of three-bedroom units and four-bedroom units.

1. Define variables for the number of three-bedroom and four-bedroom units.
2. Set up a system of equations based on the given information.
3. Solve the system of equations.

Define variables for the number of three-bedroom and four-bedroom units.
Let $x$ be the number of three-bedroom units and $y$ be the number of four-bedroom units.

Set up a system of equations based on the given information.
Equation 1: The total number of units is 205. $x + y = 205$
Equation 2: The total number of bedrooms is 732. $3x + 4y = 732$

Now, substitute $x = 88$ back into the equation for $y$ : $y = 205 - 88$ $y = 117$
So, there are $\boxed{88}$ three-bedroom units and $\boxed{117}$ four-bedroom units.