1.

Question

The grocery store sells kumquats for $4.25 a pound and Asian pears for $2.25 a pound. Write an equation in standard form for the weights of kumquats k and Asian pears p that a customer could buy with $18.

Answer 1

To write an equation in standard form for the weights of kumquats \( k \) (in pounds) and Asian pears \( p \) (in pounds) a customer could buy with $18, we start with the costs of each fruit:

• Kumquats: $4.25 per pound
• Asian pears: $2.25 per pound

The total cost for the weights \( k \) and \( p \) can be represented as: \[ 4.25k + 2.25p = 18 \]

To write this equation in standard form \( Ax + By = C \), we want to eliminate the decimal points. To do this, we can multiply the entire equation by 100:

\[ 100(4.25k) + 100(2.25p) = 100(18) \] \[ 425k + 225p = 1800 \]

Now, we arrange it in the form \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers. Thus, the standard form of the equation is: \[ 425k + 225p = 1800 \]