This problem can be solved using a system of equations. Let's define:

• $x$ as the number of small dinners ordered (each costing $5.99).
• $y$ as the number of large dinners ordered (each costing $8.99).

From the problem, we know two things:

1. The total number of dinners ordered is 134: $x + y = 134$

2. The total receipts from these 134 dinners amount to $1024.66: $5.99x + 8.99y = 1024.66$

We now have the system of equations:

1. $x + y = 134$
2. $5.99x + 8.99y = 1024.66$

We can solve this system step-by-step. First, solve for $y$ in terms of $x$ using the first equation:

$y = 134 - x$

Now substitute this expression for $y$ into the second equation:

$5.99x + 8.99(134 - x) = 1024.66$

Now solve for $x$ and then $y$.

Let me calculate that for you. sympy import symbols, Eq, solve

Define variables

x, y = symbols('x y')

Define the system of equations

eq1 = Eq(x + y, 134) eq2 = Eq(5.99x + 8.99y, 1024.66)

Solve the system of equations

solution = solve((eq1, eq2), (x, y)) solutionThe solution to the system of equations is:

• $x = 60$ small dinners ordered
• $y = 74$ large dinners ordered

So, 60 small dinners and 74 large dinners were ordered.

Would you like any further explanation or have additional questions on this topic?

Here are 5 related questions to expand your understanding:

1. How do you solve systems of equations using substitution or elimination?
2. What happens if the prices of the dinners were changed?
3. How do you solve systems of equations involving decimals and fractions?
4. Can this problem be solved with matrices?
5. How would you solve this if there were more than two types of dinners?

Tip: When dealing with word problems, always define your variables clearly and translate the problem into a system of equations for easy solving.