3.

Question

The grocery store sells kumquats for $5.00 a pound and Asian pears for $3.25 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 the equation in standard form for the weights of kumquats \( k \) (in pounds) and Asian pears \( p \) (in pounds), we need to consider the prices of each fruit.

Kumquats are priced at $5.00 per pound, and Asian pears are priced at $3.25 per pound. The total amount spent on kumquats and Asian pears should equal $18.

The cost of kumquats can be expressed as \( 5k \) and the cost of Asian pears can be expressed as \( 3.25p \). Therefore, the equation representing the total cost is:

\[ 5k + 3.25p = 18 \]

To convert this equation to standard form, which is typically expressed as \( Ax + By = C \) where \( A \), \( B \), and \( C \) are integers, we can multiply the entire equation by 4 to eliminate the decimal in the term \( 3.25p \):

\[ 4(5k) + 4(3.25p) = 4(18) \]

This simplifies to:

\[ 20k + 13p = 72 \]

Thus, the equation in standard form is:

\[ 20k + 13p = 72 \]