Question

Write a system of equations to represent each problem situation.4. Nancy and Warren are making large pots of chicken noodle soup. Nancy opens 4 largecans and 6 small cans of soup and pours them into her pot. Her pot contains 115 ounces ofsoup. Warren opens 3 large cans and 5 small cans of soup. His pot contains 91 ounces ofsoup. How many ounces of soup does each large can and each small can contain?

Answer 1

Let 'x' represents large cans

Let 'y' represents small cans.

Let us write the equation for Nancy's pots of soup,

$4x+6y=115$

Let us write the equation for Warren's pot of soup,

$3x+5y=91$

Let's combine the two equations together,

$\begin{gathered} 4x+6y=115\ldots\ldots\text{.}.1 \\ 3x+5y=91\ldots\ldots\ldots2 \end{gathered}$

Using the elimination method of the simultaneous equation to resolve them and solve for x and y.

$\begin{gathered} \text{From the equation, make the coefficient of x in the two equations the same } \\ by\text{ multiplying equation 1 by 3 and equation 2 by 4} \end{gathered}$

$\begin{gathered} 4x+6y=115\ldots\ldots.1\times3 \\ 3x+5y=91\ldots\ldots\ldots2\times4 \\ \\ 12x+18y=345\ldots\ldots\text{.}.3 \\ 12x+20y=364\ldots\ldots\ldots4 \end{gathered}$

Now, let's subtract equation 3 from 4.

$\begin{gathered} 20y-18y=364-345 \\ 2y=19 \\ y=\frac{19}{2}=9.5 \end{gathered}$

Let's solve for 'x' by substitu