Question

A florist must make 5 identical bridesmaid bouquets for a wedding. The budget is $160, and each bouquet must have 12 flowers. Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each. The florist wants twice as many roses as the other two types of flowers combined. Use r for roses, l for lilies, and i for irises. Which of the following is an incorrect equation to the system of linear equation?

A) 2.5r+4l+2i=160
B) r+l+i=12
C) r=2(l+i)
D) 2r+4l+2i=160

Answer 1

The incorrect equation is D) 2r + 4l + 2i = 160 because it does not accurately represent the cost for a single bouquet, which should be $32, not $160.

Step-by-step explanation:

The student asks for the identification of the incorrect equation within a system of linear equations designed to help a florist make 5 identical bridesmaid bouquets with a budget of $160, where each bouquet must consist of 12 flowers with specific costs per type of flower and a condition that there should be twice as many roses as lilies and irises combined. We can represent the quantities of roses, lilies, and irises as r, l, and i, respectively.

The correct equations derived from the problem statement would be:

• $2.50r + $4l + $2i = $32 (Because $160 budget for 5 bouquets translates to $32 per bouquet)
• r + l + i = 12 (The number of flowers per bouquet)
• r = 2(l + i) (Twice as many roses as the other two types combined)

By looking at the provided options and comparing them to these equations, the option D) 2r + 4l + 2i = 160 is incorrect because it does not reflect the calculation for a single bouquet's cost but rather incorrectly scales the amounts by number of flowers instead of accounting for the cost of each type.