\( \begin{array}{l}\text { An order of brown rice and quinoa weighs } 17 \text { pounds and costs } \$ 54 \text {. } \\ \text { Brown rice: } \$ 2.00 \text { per pound } \\ \text { Quinoa: } \$ 4.50 \text { per pound } \\ \text { How many pounds of brown rice and quinoa are in this order? }\end{array} \) One way to solve this system is to substitute the value of one variable into the other equation. To do this, we can use either variable, \( q \) or \( b \). So, we need to know either: \( q= \) some value, so that we can substitute that value for \( q \), or, \( b= \) some value, so that we can substitute that value for \( b \). Is either equation written as \( q \) equals some value or \( b \) equals some value yet?

To solve the problem, we need to set up a system of equations based on the information provided. Let's define our variables: - Let \( b \) be the number of pounds of brown rice. - Let \( q \) be the number of pounds of quinoa. From the problem, we have the following two equations: 1. The total weight of the order: \[ b + q = 17 \] 2. The total cost of the order: \[ 2b + 4.5q = 54 \] Now, we can express one variable in terms of the other using the first equation. Let's solve for \( q \): \[ q = 17 - b \] Now we can substitute this expression for \( q \) into the second equation. Let's do that step by step. Substituting \( q \) into the cost equation: \[ 2b + 4.5(17 - b) = 54 \] Now, let's simplify and solve for \( b \): 1. Distribute \( 4.5 \): \[ 2b + 76.5 - 4.5b = 54 \] 2. Combine like terms: \[ -2.5b + 76.5 = 54 \] 3. Subtract \( 76.5 \) from both sides: \[ -2.5b = 54 - 76.5 \] \[ -2.5b = -22.5 \] 4. Divide by \( -2.5 \): \[ b = \frac{-22.5}{-2.5} = 9 \] Now that we have \( b \), we can find \( q \): \[ q = 17 - b = 17 - 9 = 8 \] Thus, the solution is: - Brown rice: \( 9 \) pounds - Quinoa: \( 8 \) pounds To summarize: - The order contains \( 9 \) pounds of brown rice and \( 8 \) pounds of quinoa.