Question

1. jack and shanice are selling flower bulbs for a school fundraiser. customers can buy bags of windflower bulbs and packages of crocus bulbs. jack sold 4 bags of windflower bulbs and 10 packages of crocus bulbs for a total of $166. shanice sold 13 bags of windflower bulbs and 2 packages of crocus bulbs for a total of $82. find the cost each of one bag of windflower bulbs and one package of crocus bulbs.

Explanation:

Step1: Define Variables

Let \( w \) be the cost of one bag of windflower bulbs and \( c \) be the cost of one package of crocus bulbs.

Step2: Set Up Equations

From Jack's sales: \( 4w + 10c = 166 \)
From Shanice's sales: \( 13w + 2c = 82 \)

Step3: Solve the System of Equations

First, simplify the first equation: divide by 2, get \( 2w + 5c = 83 \) (Equation 1)
Second, multiply the second equation by 5: \( 65w + 10c = 410 \) (Equation 2)
Multiply Equation 1 by 2: \( 4w + 10c = 166 \) (Equation 3)
Subtract Equation 3 from Equation 2: \( 61w = 244 \)
Solve for \( w \): \( w = \frac{244}{61} = 4 \)

Step4: Find \( c \)

Substitute \( w = 4 \) into Equation 1: \( 2(4) + 5c = 83 \)
\( 8 + 5c = 83 \)
\( 5c = 75 \)
\( c = 15 \)

Answer:

One bag of windflower bulbs costs $4, and one package of crocus bulbs costs $15.