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9 January, 05:49

Dr. Gonzalez is considering joining the Garden Club. If he pays a $25 membership fee, he

can buy rosebushes from the club at a reduced price of $10 each. If he does not join the

club, he can buy rosebushes from a local nursery for $15 each. The graph below compares

the cost of buying rosebushes from the Garden Club and from the local nursery.

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Answers (1)
  1. 9 January, 08:19
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    In the Garden Club the cost will be a fixed fee of $25 and $10 for each rosebush, so if he buys X rosebushes, the total cost will be:

    C1 (X) = $25 + $10*X

    While in the local nursery there is no initial cost, and each rosebush costs $15, so if he buys X rosebushes, the total cost will be:

    C2 (X) = $15*X

    Now, let's find the value of X where C1 and C2 are equal, this is:

    $25 + $10*X = $15*X

    $25 = $15*X - $10*X = $5*X

    X = 25/5 = 5

    This means that if he buys 5 rosebushes, he will pay the same amount in both places.

    If he buys less than 5 rosebushes, he will pay less in the local nursery (as it has a bigger slope, but no initial fee)

    If he buys more than 5 rosebushes, he will pay less in the Garden club (because it has a smaller slope)
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