5. Carlos and Mike are selling cheesecakes for a school fundraiser. Customers can buy pecan cheesecakes and apple cheesecakes. Carlos sold 1 pecan cheesecake and 4 apple cheesecakes for a total
of $44. Mike sold 14 pecan cheesecakes and 14 apple cheesecakes for a total of $238. Find the cost
each of one pecan cheesecake and one apple cheesecake.
a. Define variables:
b. System:
c. Solve the systems (optional):

One pecan costs $8. One apple costs $9.

Step-by-step explanation:

p and a are number of number of pecan and apple sold, respectively.

"1 pecan cheesecake and 4 apple cheesecakes for $44"

p + 4a = 44

"14 pecan cheesecakes and 14 apple cheesecakes for $238"

14p + 14a = 238

You have a system of two equations in two unknowns:

p + 4a = 44

14p + 14a = 238

Eliminate the p terms: Multiply the first equation by -14, then add the product to the second equation.

-14p  - 56a = -616

 14p + 14a = 238

  -42a = -378

a = (-378)/(-42) = 9

p = 44-4a = 8

One pecan costs $8. One apple costs $9.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.