How Many Cookies Did Tim Eat on the First Day?

[medeco]

Hello,
I would love to get help or a formula to help figure out my son's word problem he arrived with this afternoon for Homework on his first day back to school here in Georgia.

The problems is:

Tim ate 100 cookies in 5 days. Each day he ate 6 more than he did the day before.
How many cookies did he eat on the 1st day?

Please help me help my son solve this problem.
Thanks,
Pat
E-mail: dcvgnola@yahoo.com

 

[Cesium]

Hi there,

Each day Tim eats six more cookies than the previous one.

Let x = the number of cookies Tim ate on the first day
x+6 = 2nd day
x+12 = 3rd day
x+18= 4th day
x+24 = 5th day

x + (x+6) + (x+12) + (x+18) + (x+24) = 100
5x + 60 = 100

Your son should be able to figure it out from there. Solve that equation and that's your answer. Make sense?

 

[tacman]

Hi Pat,

Thank you for reaching out for help with your son's math problem. I would be happy to assist you and your son in solving this word problem.

To solve this problem, we can use a formula called the arithmetic sequence formula. This formula helps us find the value of each term in a sequence when we know the first term and the common difference between each term.

In this problem, the first term is the number of cookies Tim ate on the first day, and the common difference is the number of cookies he ate more each day. So, the formula we will use is: a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the number of the term we want to find, and d is the common difference.

In this case, we know that a_1 = the number of cookies Tim ate on the first day, n = 5 (since there are 5 days in total), and d = 6 (since he ate 6 more cookies each day). So, we can plug in these values into the formula and solve for a_1.

a_5 = a_1 + (5-1)*6
100 = a_1 + 4*6
100 = a_1 + 24
a_1 = 76

Therefore, Tim ate 76 cookies on the first day.

I hope this explanation helps you and your son understand how to solve this problem. Please let me know if you have any further questions or need more clarification. Best of luck to your son on his first day back to school!

Best regards,