149k views
5 votes
Kaley and Natalia are participating in a challenge to see who can collect the most cans of food to donate.Kaley has already collected 14 cans and has set a goal to collect 3more each day.Natalia has collected 6 cans and has set a goal to collect 4 more each day

User Dozatron
by
7.9k points

1 Answer

6 votes

Final answer:

Kaley and Natalia are participating in a food collection challenge. Kaley starts with 14 cans, Natalia with 6. After 8 days, both will have collected 38 cans, after which Natalia will begin to collect more than Kaley due to her higher daily collection rate.

Step-by-step explanation:

Kaley and Natalia are participating in a challenge to see who can collect the most cans of food to donate. Kaley has already collected 14 cans and is collecting 3 more each day. Natalia has collected 6 cans and is collecting 4 more each day. To analyze who will collect more cans and when, we can define two linear equations based on their initial numbers of cans and their daily collection rates:

  • Kaley's cans = 14 + 3d, where d represents days.
  • Natalia's cans = 6 + 4d.

By setting the two equations equal to each other, we can determine when Natalia will catch up to Kaley or if Kaley will continue to lead.

14 + 3d = 6 + 4d

This can be solved as follows:

  • Subtract 3d from both sides: 14 = 6 + d
  • Subtract 6 from both sides: 8 = d

Thus, after 8 days, Natalia will have the same number of cans as Kaley. To find out who will have more after 8 days, we need to continue collecting: Kaley will have 14 + (3 × 8) = 38 cans, and Natalia will have 6 + (4 × 8) = 38 cans.

After this point, since Natalia's daily collection rate is higher, she will surpass Kaley in the number of cans collected.

User FrederickCook
by
9.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories