Question

Cora and Isabelle are both selling cookie dough for a fundraiser. Although Cora has alreadysold 9 tubs, Isabelle hasn't sold any yet. If Cora starts selling 2 tubs per day and Isabellebegins selling 5 tubs per day, they will eventually sell the same amount of cookie dough. Howmany tubs will each sell? How many days will that take?

Answer 1

We will solve, by writing the functions described in the text:

`S_c=2d+9`

This function describes Cora's sales, where d is the number of days and 9 is the amount she already sold.

And:

`S_i=5d`

This function describes Isabelle's sales, where d is the number of days.

In order to determine at what day they would have sold the same amount of cookies, we equal them:

`2d+9=5d`

Now, we solve for d:

`\Rightarrow9=5d-2d\Rightarrow9=3d\Rightarrow d=3`

From this, we can see that it would take them 3 days to sell the same number of cookies, and in order to know the number of cookies, we replace the number of days we found in one of the original functions, that is:

`S_c=2(3)+9\Rightarrow S_c=15`

And to corroborate:

`S_i=5(3)\Rightarrow S_i=15`

So, they would have sold 15 tubes when they have sold the same amount.