Systems of Equations Problem

Question

You want to order 3 pounds of ham, and 2 pounds of turkey, how much does ham cost? How much does turkey cost?

 

Customer 1 ordered .5 pounds of turkey and 1 pound of ham. Their total cost was $8.50

 

Customer 2 ordered 2 pounds of turkey and 4 pounds of ham. Their total cost was $34

 

What would your total cost?

Answer 1

Let t be the price of turkey per pound and h be the same for ham

Customer 1: 0.5t + 1h = 8.50 ---> h = 8.50 - 0.5t
Customer 2: 2t + 4h = 34
You: 3h + 2t = ???

Notice that customer 2 ordered 4 times what customer 1 asked for. This means that both equation (c1 and C2) are the same. Therefore, there is an infinite number of theoretical solutions to this problem.

 

For simplicity, t + 2h = 17, so I will let t be $7.00, which would make h be $5.00

Using the above values, your order's price is as follows:

3($5.00) + 2($7.00) = 15 + 14 = $29.00

 

Answer 2

First equation based on givens:  0.5T + H = 8.50

Second equation:                        2T  + 4H = 34.

 

Can you guess what T and H mean?

 

Solving this system will determine T & H; then you can compute your total cost for your specific order.

 

Have you ever encountered the standard advice given in Algebra, to FIRST CHOOSE LETTER (names) for the Unknowns?