Caroline knows that the more educational workshops she hosts at the giraffe exhibit, the more donations people make to the giraffes, which helps fund their care. However, she's worried because when the female giraffe gives birth, they'll have to stop doing the educational workshops for a few weeks to let the baby giraffe acclimate.

Question

Last week, Caroline held 12 educational workshops and the giraffes received $1,643 of donations. This week, she held 9 educational workshops and the giraffes received $1,364 of donations.
In #1, how much can Caroline expect in donations when she does NO educational workshops?

$93

$0

$279

$527

GPT-4o mini · Answer

To find out how much Caroline can expect in donations when she does no educational workshops, we can use the data provided from the two weeks to determine the relationship between the number of workshops and the amount of donations.

Let $ w $ represent the number of educational workshops and $ d $ represent the amount of donations. We can set up the following equations based on the information provided:

For 12 workshops: \[ d = mw + b \] Where:

$ m $ is the slope (change in donations per workshop)
$ b $ is the y-intercept (donations when no workshops are held)

This gives us the equation: \[ 1643 = 12m + b \] (1)

For 9 workshops: \[ 1364 = 9m + b \] (2)

Now we have a system of two equations. We can solve for $ m $ and $ b $.

Subtract equation (2) from equation (1) to eliminate $ b $:

\[ 1643 - 1364 = (12m + b) - (9m + b) \] \[ 279 = 3m \]

Solving for $ m $: \[ m = \frac{279}{3} = 93 \]

Now we can substitute $ m $ back into one of the equations to find $ b $. Using equation (1): \[ 1643 = 12(93) + b \] \[ 1643 = 1116 + b \] \[ b = 1643 - 1116 = 527 \]

Therefore, when Caroline does no educational workshops (i.e., when $ w = 0 $), the expected donations $ b $ would be:

\[ \boxed{527} \]