Question

Jessica ordered 10 bouquets of tulips, 4 bouquets of roses, and 6 bouquets of lilies for a total of $670. The combined cost to buy one of each type of bouquet is $115. If a bouquet of lilies costs $5 more than a bouquet of tulips, what is the cost of each type of flower bouquet? A. The cost of one bouquet of tulips is $30, one bouquet of roses is $60, and one bouquet of lilies is $25. B. The cost of one bouquet of tulips is $25, one bouquet of roses is $30, and one bouquet of lilies is $60. C. The cost of one bouquet of tulips is $25, one bouquet of roses is $60, and one bouquet of lilies is $30. D. The cost of one bouquet of tulips is $26, one bouquet of roses is $60, and one bouquet of lilies is $31.

Answer 1

Answer:C

Explanation:

Let x represent the cost of a bouquet of tulips.

Let y represent the cost of a bouquet of roses.

Let z represent the cost of a bouquet of lilies.

Jessica ordered 10 bouquets of tulips, 4 bouquets of roses, and 6 bouquets of lilies for a total of $670. This means that

10x + 4y + 6z = 670 - - - - - - - - - 1

The combined cost to buy one of each type of bouquet is $115. This means that

x + y + z = 115- - - - - - - - - 2

If a bouquet of lilies costs $5 more than a bouquet of tulips, it means that

z = x + 5 - - - - - - - - - 3

Substituting equation 3 into equation 1 and equation 2, it becomes

10x + 4y + 6(x+5)= 670

10x +4y + 6x + 30 = 670

16x + 4y = 670 - 30

16x + 4y = 640 = - - - - - - - - - 4

Substituting equation 3 into equation 2, it becomes

x + y + x + 5 =

2x + y = 115 - 5

2x + y = 110 - - - - - - - - - 5

Multiplying equation 5 by 4 , it becomes

8x + 4y = 440 - - - - - - - - - 6

Subtracting equation 6 from equation 4, it becomes

8x = 200

x = 200/8 = 25

2x + y = 110

2×25 + y = 110

50 + y = 110

y = 110 - 50 = 60

z = x + 5

z = 25 + 5 = 30

The cost of one bouquet of tulips is $25, one bouquet of roses is $60, and one bouquet of lilies is $30.