Trisha and Baldwin have summer jobs selling newspaper subscriptions door-to-door, but their compensation plans are different. Trisha earns a base wage of $11 per hour, as well as $2 for every subscription that she sells. Baldwin gets $3 per subscription sold, in addition to a base wage of $7 per hour. If they each sell a certain number of subscriptions in an hour, they will end up earning the same amount. How much would each one earn? How many subscriptions would that be?

Question

GPT 3.5 · Answer

Let's assume that Trisha sells x subscriptions in an hour.

Trisha's earnings from selling subscriptions would be $2 * x.
Her total earnings in an hour would be $11 base wage + $2 * x subscriptions.

Similarly, let's assume that Baldwin sells y subscriptions in an hour.

Baldwin's earnings from selling subscriptions would be $3 * y.
His total earnings in an hour would be $7 base wage + $3 * y subscriptions.

Since they earn the same amount, we can set up the equation:

11 + 2x = 7 + 3y

Rearranging the equation, we have:

2x - 3y = -4

Now, we need to find the values of x and y that satisfy this equation.

We can start by checking possible values of x and calculating the corresponding value of y. We can then find the point where the equation is satisfied. We can choose a value for x and then calculate the corresponding value of y, or vice versa.

Let's try x = 2:

2 * 2 - 3y = -4
4 - 3y = -4
-3y = -8
y = 8/3

So, if Trisha sells 2 subscriptions in an hour, Baldwin would need to sell 8/3 subscriptions in an hour for them to earn the same amount.

Now, let's find their earnings:

Trisha's total earnings = $11 base wage + $2 per subscription * 2 subscriptions = $11 + $4 = $15

Baldwin's total earnings = $7 base wage + $3 per subscription * (8/3) subscriptions = $7 + $8 = $15

Therefore, both Trisha and Baldwin would earn $15 if Trisha sells 2 subscriptions and Baldwin sells 8/3 subscriptions.