Jason has some chocolate and macadamia nuts cookies. If he sells
16 chocolate cookies and 4 macadamia nuts cookies a day, he would have 65 chocolate cookies left by the time all the macadamia nuts cookies are sold. If he sells 8 macadamia nuts cookies and 4 chocolate cookies a day, he would have 289 chocolate cookies left by the time all the macadamia nuts cookies are sold. How many chocolate cookies does he have?
To solve this problem, we can set up a system of equations. Let's assume that Jason starts with c chocolate cookies and m macadamia nuts cookies.
From the first scenario, we know that if he sells 16 chocolate cookies and 4 macadamia nuts cookies a day, he would have 65 chocolate cookies left by the time all the macadamia nuts cookies are sold. This can be represented by the equation:
c - 16d = 65 (equation 1)
where d is the number of days it takes to sell all the macadamia nuts cookies.
Similarly, from the second scenario, we know that if he sells 8 macadamia nuts cookies and 4 chocolate cookies a day, he would have 289 chocolate cookies left by the time all the macadamia nuts cookies are sold. This can be represented by the equation:
c - 4d = 289 (equation 2)
To find the number of chocolate cookies Jason has, we need to solve these equations simultaneously. We can do this by solving for c in both equations and then equating the expressions.
From equation 1, we can solve for c:
c = 65 + 16d
Substituting this value for c in equation 2, we get:
65 + 16d - 4d = 289
Combining like terms, we have:
12d = 224
Dividing both sides by 12, we find:
d = 18.67
Since d represents the number of days, it cannot be a decimal or fraction. We can round it to the nearest whole number, which is 19.
Now, we can substitute d = 19 back into equation 1 to find the number of chocolate cookies:
c = 65 + 16(19)
c = 65 + 304
c = 369
Therefore, Jason has 369 chocolate cookies.