Question

Ted and Jessica each improved their yards by planting hostas and ivy. They bought their supplies from the same store. Ted spent $210 on 10 hostas and 13 pots of ivy. Jessica spent $116 on 2 hostas and 10 pots of ivy. Find the cost of one hosta and the cost of one pot of ivy.

A) The cost of one hosta is $10, and the cost of one pot of ivy is $8.
B) The cost of one hosta is $8, and the cost of one pot of ivy is $10.
C) The cost of one hosta is $15, and the cost of one pot of ivy is $5.
D) The cost of one hosta is $5, and the cost of one pot of ivy is $15

Answer 1

The cost of one hosta is $2.50, and the cost of one pot of ivy is $30/37.

Step-by-step explanation:

To find the cost of one hosta and the cost of one pot of ivy, we can set up a system of equations. Let's let h represent the cost of one hosta and i represent the cost of one pot of ivy.

From Ted's purchases: 10h + 13i = 210

From Jessica's purchases: 2h + 10i = 116

Now we can solve this system of equations to find the values of h and i.

Subtracting twice the second equation from the first equation, we get 10h + 13i - 4h - 20i = 210 - 2(116), simplifying to 6h - 7i = -12.

Rearranging this equation gives us 6h = 7i - 12, or h = (7i - 12)/6 = (7/6)i - 2. Substituting this expression for h into the second equation, we get 2((7/6)i - 2) + 10i = 116, which simplifies to (7/3)i - 4 + 10i = 116.

Combining like terms, we have (37/3)i - 4 = 116.

Adding 4 to both sides gives us (37/3)i = 120.

Dividing by (37/3), we find i = 120 * (3/37) = 30/37.

Substituting this value of i into the expression for h, we get h = (7/6)(30/37) - 2 = 5/2.

Therefore, the cost of one hosta is $5/2 = $2.50, and the cost of one pot of ivy is $30/37.