Question

Jan and Wayne went to the store to buy some groceries. Jan bought 2 cans of corn beef hash and 3 cans of creamed chipped beef for $4.95. Wayne bought 3 cans of corn beef hash and 2 cans of creamed chipped beef for $5.45. Let H represent the price of a can of corn beef hash, and C represent the price of a can of creamed chipped beef. Which system of equations models the word problem on the left?

Answer 1

Answer:

The system of equations that models the problem is:

$\left \{ {{2*H+3*C=4.95} \atop {3*H+2*C=5.45}} \right.$

Step-by-step explanation:

A system of equations is a set of two or more equations with several unknowns in which we want to find a common solution. So, a system of linear equations is a set of (linear) equations that have more than one unknown that appear in several of the equations. The equations relate these variables or unknowns to each other.

In this case, the unknown variables are:

• H: price of a can of corn beef hash
• C: price of a can of creamed chipped beef

Knowing the unit price of a product, the price of a certain quantity of that product is calculated by multiplying that quantity by the unit price. So the price for 2 cans of ground beef hash can be calculated as 2 * H and the price for 3 cans of ground beef with cream can be calculated as 3 * C. Jan paid $ 4.95 for those amounts from both cans. This means that the sum of the can prices must be $ 4.95. So: 2*H + 3*C= 4.95 Equation (A)

Thinking similarly, if Wayne bought 3 cans of corn beef hash and 2 cans of creamed chipped beef for $5.45, Wayne's buy can be expressed by the equation:

3*H + 2*C= 5.45 Equation (B)

Finally, the system of equations that models the problem is:

$\left \{ {{2*H+3*C=4.95} \atop {3*H+2*C=5.45}} \right.$