Math / Algebra

QuestionA party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 6 tables is $\$ 42$ . The total cost to rent 5 chairs and 3 tables is $\$ 30$ . What is the cost to rent each chair and each table?
Cost to rent each chair: $\$$ $\square$ Cost to rent each table: $\$$ $\square$

Studdy Solution

STEP 1

1. Let the cost to rent each chair be $x$ dollars.
2. Let the cost to rent each table be $y$ dollars.
3. The total cost to rent 2 chairs and 6 tables is $42.<br />4. The total cost to rent 5 chairs and 3 tables is$ 30.
5. We need to find the values of $x$ and $y$ .

STEP 2

1. Set up a system of equations based on the given information.
2. Solve the system of equations using substitution or elimination method.
3. Verify the solution.

STEP 3

Set up a system of equations based on the given information.
From the problem statement, we can write the following equations: $2x + 6y = 42$ $5x + 3y = 30$

STEP 4

Solve the system of equations using the elimination method.
First, let's eliminate one of the variables. We can eliminate $y$ by making the coefficients of $y$ in both equations equal.
Multiply the first equation by 1 and the second equation by 2: $2x + 6y = 42$ $10x + 6y = 60$
Now subtract the first equation from the second equation: $(10x + 6y) - (2x + 6y) = 60 - 42$ $8x = 18$

STEP 5

Solve for $x$ .
Divide both sides by 8: $x = \frac{18}{8}$ $x = 2.25$

STEP 6

Substitute $x = 2.25$ back into one of the original equations to solve for $y$ .
Using the first equation: $2(2.25) + 6y = 42$ $4.5 + 6y = 42$
Subtract 4.5 from both sides: $6y = 37.5$
Divide by 6: $y = \frac{37.5}{6}$ $y = 6.25$

STEP 7

Verify the solution by substituting $x = 2.25$ and $y = 6.25$ into the second original equation.
$5(2.25) + 3(6.25) = 30$ $11.25 + 18.75 = 30$ $30 = 30$
The solution satisfies both equations.
Cost to rent each chair: \$$\boxed{2.25}$ Cost to rent each table: \$$\boxed{6.25}$

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Studdy Solution

STEP 1

1. Let the cost to rent each chair be $x$ dollars.
2. Let the cost to rent each table be $y$ dollars.
3. The total cost to rent 2 chairs and 6 tables is $42.<br />4. The total cost to rent 5 chairs and 3 tables is$ 30.
5. We need to find the values of $x$ and $y$ .

STEP 2

1. Set up a system of equations based on the given information.
2. Solve the system of equations using substitution or elimination method.
3. Verify the solution.

STEP 3

Set up a system of equations based on the given information.
From the problem statement, we can write the following equations: $2x + 6y = 42$ $5x + 3y = 30$

STEP 4

STEP 5

Solve for $x$ .
Divide both sides by 8: $x = \frac{18}{8}$ $x = 2.25$

STEP 6

Substitute $x = 2.25$ back into one of the original equations to solve for $y$ .
Using the first equation: $2(2.25) + 6y = 42$ $4.5 + 6y = 42$
Subtract 4.5 from both sides: $6y = 37.5$
Divide by 6: $y = \frac{37.5}{6}$ $y = 6.25$

STEP 7

Verify the solution by substituting $x = 2.25$ and $y = 6.25$ into the second original equation.
$5(2.25) + 3(6.25) = 30$ $11.25 + 18.75 = 30$ $30 = 30$
The solution satisfies both equations.
Cost to rent each chair: \$\(\boxed{2.25}\) Cost to rent each table: \$\(\boxed{6.25}\)

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Studdy Solution

STEP 1

STEP 2

1. Set up a system of equations based on the given information.2. Solve the system of equations using substitution or elimination method.3. Verify the solution.

STEP 3

Set up a system of equations based on the given information.From the problem statement, we can write the following equations: 2x+6y=42 2x + 6y = 42 2x+6y=42 5x+3y=30 5x + 3y = 30 5x+3y=30

STEP 4

STEP 5

Solve for x x x.Divide both sides by 8: x=188 x = \frac{18}{8} x=818​ x=2.25 x = 2.25 x=2.25

STEP 6

STEP 7

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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. Set up a system of equations based on the given information.
2. Solve the system of equations using substitution or elimination method.
3. Verify the solution.

Set up a system of equations based on the given information.
From the problem statement, we can write the following equations: $2x + 6y = 42$ $5x + 3y = 30$

Solve for $x$ .
Divide both sides by 8: $x = \frac{18}{8}$ $x = 2.25$