Question

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.

Answer 1

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)