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2 April, 15:31

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?

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  1. 2 April, 16:59
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    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
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