Question

Brown rice costs $2 per pound, and beans cost $1.60 per pound. Lin has $10 to spend on these items to make a large meal of beans and rice for a potluck dinner. Let b be the number of pounds of beans Lin buys and r be the number of pounds of rice she buys when she spends all her money on this meal

Answer 1

1.
`2r+1.6b=10`

2.
`r=5-0.8b`

3.
`b=6.25-1.25r`

Explanation:

The complete exercise is: "Brown rice costs $2 per pound, and beans cost $1.60 per pound. Lin has $10 to spend on these items to make a large meal of beans and rice for a potluck dinner. Let b be the number of pounds of beans Lin buys and r be the number of pounds of rice she buys when she spends all her money on this meal.

1. Write an equation relating the two variables.

2. Rearrange the equation so "b" is the independent variable.

3. Rearrange the equation so "r" is the independent variable."

1. According to the information exercise given in the exercise, the cost per pounds of brown rice is $2. Since "r" represents the number of pounds of rice Lin buys, the total cost of the brown rice she buys can be represented with this expression:

`2r`

The beans cost $1.60 per pound. Since "b" represents the number of pounds of beans Lin buys, the total cost of beans she buys can be represented as:

`1.6b`

Knowing that she spends $10, you can write the following equation:

`2r+1.6b=10`

2. In order to rearrange the equation so "b" is the independent variable, you need to solve for "r":

`2r+1.6b=10\\\\2r=10-1.6b\\\\r=(10-1.6b)/(2) \\\\r=5-0.8b`

3. To rearrange the equation so "r" is the independent variable, you must solve for "b". You get:

`2r+1.6b=10\\\\1.6b=10-2r\\\\b=(10-2r)/(1.6)\\\\b=6.25-1.25r`