$$ \begin{array}{l} ext { An order of brown rice and quinoa weighs } 17 ext { pounds and costs } \$ 54 ext {. } \ ext { Brown rice: } \$ 2.00 ext { per pound } \ ext { Quinoa: } \$ 4.50 ext { per pound } \ ext { How many pounds of brown rice and quinoa are in this order? }\end{array} $$ 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?

Question

$$ \begin{array}{l}	ext { An order of brown rice and quinoa weighs } 17 	ext { pounds and costs } \$ 54 	ext {. } \ 	ext { Brown rice: } \$ 2.00 	ext { per pound } \ 	ext { Quinoa: } \$ 4.50 	ext { per pound } \ 	ext { How many pounds of brown rice and quinoa are in this order? }\end{array} $$ 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?

UpStudy AI · Accepted Answer

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.
There are 9 pounds of brown rice and 8 pounds of quinoa in the order.

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