Math Snap

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.
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:
$$y = \frac{37.5}{6}$$ $$y = 6.25$$

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}$