Question

1. mallory and eugene each improved their yards by planting roses and ivy. they bought their supplies from the same store. mallory spent $208 on 14 rose bushes and 12 pots of ivy. eugene spent $152 on 13 rose bushes and 6 pots of ivy. find the cost of one rose bush and one the cost of one pot of ivy.

Explanation:

Step1: Define variables

Let \( r \) be the cost of one rose bush (in dollars) and \( i \) be the cost of one pot of ivy (in dollars).

Step2: Set up equations

From Mallory's purchase: \( 14r + 12i = 208 \) (Equation 1)
From Eugene's purchase: \( 13r + 6i = 152 \) (Equation 2)

Step3: Simplify Equation 2

Multiply Equation 2 by 2: \( 26r + 12i = 304 \) (Equation 3)

Step4: Subtract Equation 1 from Equation 3

\( (26r + 12i) - (14r + 12i) = 304 - 208 \)
\( 26r + 12i - 14r - 12i = 96 \)
\( 12r = 96 \)

Step5: Solve for \( r \)

Divide both sides by 12: \( r = \frac{96}{12} = 8 \)

Step6: Substitute \( r = 8 \) into Equation 2

\( 13(8) + 6i = 152 \)
\( 104 + 6i = 152 \)

Step7: Solve for \( i \)

Subtract 104 from both sides: \( 6i = 152 - 104 = 48 \)
Divide by 6: \( i = \frac{48}{6} = 8 \)

Answer:

The cost of one rose bush is \$8 and the cost of one pot of ivy is \$8.