Question

3) Billy's Restaurant ordered 210 flowers for Mother's Day. They ordered carnations at $1.50 each, roses at $5.75 each, and daisies at $2.60 each. They ordered mostly carnations, and 20 fewer daisies than roses. The total order came to $667.50. How many of each type of flower was ordered?

Answer 1

Total number of flowers = 210

Carnations = c = $1.50

Roses = r = $5.75

Daisies = d = $2.60

d = r - 20

Total price = $667.5

Equation 1

1.5c + 5.75r + 2.6d = 667.5

Equation 2

c + r + d = 210

Equation 3

d = r - 20

Solve by substitution

1.5c + 5.75r + 2.6(r - 20) = 667.5

1.5c + 5.75r + 2.6r - 52 = 667.5

1.5c + 8.35r = 667.5 + 52

1.5c + 8.35r = 719.5

c + r + r - 20 = 210

c + 2r = 210 + 20

c + 2r = 230

Solve for c

x c = 230 - 2r

1.5(230 - 2r) + 8.35r = 719.5

345 - 3r + 8.35r = 719.5

5.35r = 719.5 - 345

5.35r = 374.5

r = 374.5/5.35

r = 70

e c = 230 - 2(70)

c = 230 - 140

c = 90

d = 70 - 20

d = 50

Billy ordered 70 roses, 90 carnations and 50 daisies.

5

345 - 3r + 8.35r = 719.5

5.35r = 719.5 - 345

5.35r = 374.5

r = 374.5/5.35

r = 70

e c = 230 - 2(70)

c = 230 - 140

c = 90

d = 70 - 20

d = 50

Billy ordered 70 roses, 90 carnations and 50 daisies.