Step by Step Homework Help Please

Question

A restaurant charged one customer $28.20 for 3 small dishes and 5 large

dishes and charged another customer $23.30 for 4 small dishes and 3 large

dishes. Write the linear equations and find the cost of a small dish and a

large dish.

b) What will 2 small and 4 large dishes cost?

I have 3 of these can i please get a step by step very much appreciated.

Answer 1

1) 3s + 5l = 28.20

2) 4s + 3l = 23.30

I choose to solve for l.

Multiply 1) by 4 and 2) by 3

4) 12s + 20l = 112.80

5) 12s + 9l = 69.9

Subtract 5) from 4)

6) 11l = 42.9

7) l = 3.9

A large meal cost $3,90

Answer 2

These are common problems in SAT and ACT math. Your step-by-step process is to:

(1) Find a way to write what you are give as equations. Typically, you will have two equations with two unknowns.

(2) Use algebra to combine the equations in a way that eliminates one of the variables.

(3) Solve for that variable.

(4) Use that result to solve for the other variable.

In this case you can represent what you're given by:

3s + 5l = 28.20 and

4s + 3l = 23.30

One easy way to do this that I like is to set up the equations so that by adding them together, or subtracting one from the other, you can eliminate a variable. You can then solve for the remaining variable, etc.

However, when asked for something as in this case, that amounts to finding 2s + 4l = ?, then see if you can get to that or something like it without finding the individual variables. In this case, simply by subtracting one equation from the other, you get to something useful:

(3s + 5l = 28.20)

-(4s + 3l = 23.30)

________________

s + 2l = 4.90

The key here is to recognize that you can multiply that outcome by 2 to find the answer needed.

That means that 2s + 4l = 2 x 4.90 = $9.80