Sumalee and Scott each improved their yards by planting daylilies and ivy. They bought their supplies from the same store. Sumalee spent $93 on 6 daylilies and 3 pots of ivy. Scott spent
$196 on 13 daylilies and 6 pots of ivy. Find the cost of one daylily and the cost of one pot of ivy.

The cost of one daylily is $10 and the cost of one pot of ivy is $11

Step-by-step explanation:

To solve the question we will form a system of equations

Assume that the cost of 1 daylily is x and the cost of 1 pot of ivy is y

∵ Sumalee spent $93 on 6 daylilies and 3 pots of ivy

→ Multiply x by 6, y by 3, then add the products and equate the sum by 93

∴ 6x + 3y = 93 ⇒ (1)

∵ Scott spent $196 on 13 daylilies and 6 pots of ivy

→ Multiply x by 13, y by 6, then add the products and equate the sum by 196

∴ 13x + 6y = 196 ⇒ (2)

Now we have a system of equations to solve it

→ Multiply equation (1) by -2

∵ -2(6x) + -2(3y) = -2(93)

∴ -12x - 6y = -186 ⇒ (3)

→ Add equations (2) and (3)

∵ (13x + -12x) + (6y + -6y) = (196 + - 186)

∴ x + 0 = 10

∴ x = 10

→ Substitute the value of x in equation (1) to find the value of y

∵ 6(10) + 3y = 93

∴ 60 + 3y = 93

→ Subtract 60 from both sides

∵ 60 - 60 + 3y = 93 - 60

∴ 3y = 33

→ Divide both sides by 3

∴ y = 11

∴ The cost of one daylily is $10 and the cost of one pot of ivy is $11

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