Eugene and Scott are selling flower bulbs for a school fundraiser. Customers can buy bags of windflower bulbs and packages of crocus bulbs. Eugene sold 14 bags of windflower bulbs and 5 packages of crocus bulbs for a total of $257. Scott sold 11 bags of windflower bulbs and 1 package of crocus bulbs for a total of $158. How much does a bag of crocus bulbs cost?

A bag of crocus bulbs costs $15

Step-by-step explanation:

Assume that x is the cost of a bag of windflower bulbs and y is the cost of a package of crocus bulbs

∵ The cost of a bag of windflower bulbs is $x

∵ The cost of a package of crocus bulbs is $y

∵ Eugene sold 14 bags of windflower bulbs and 5 packages

of crocus bulbs for a total of $257

- Multiply x by 14 and y by 5, then equate the sum of the

products by 257

∴ 14x + 5y = 257 ⇒ (1)

∵ Scott sold 11 bags of windflower bulbs and 1 package of

crocus bulbs for a total of $158

- Multiply x by 11 and y by 1, then equate the sum of the

products by 158

∴ 11x + y = 158 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (2) by - 5 to make the coefficients of y equal in value and opposite in signs

∵ - 55x - 5y = - 790 ⇒ (3)

- Add equations (1) and (3) to eliminate y

∴ - 41x = - 533

- Divide both sides by - 41

∴ x = 13

Substitute the value of x in equation (1) or (2) to find y

∵ 11 (13) + y = 158

∴ 143 + y = 158

- Subtract both sides by 143

∴ y = 15

A bag of crocus bulbs costs $15