1) Every day, Lucy collects some candies. If Lucy collects 10 candies on the first day of Halloween, and 2 more candies each subsequent day, how many candies will Lucy have collected after 7 days?

Question

1) Every day, Lucy collects some candies. If Lucy collects 10 candies on the first day of Halloween, and 2 more candies each subsequent day, how many candies will Lucy have collected after 7 days?
Solve this equation word problem showing your defined variable, equation, inverse operations to solve, and final solution with units. Please format it simply.

GPT-4o mini · Answer

**Defined Variable:** Let $ C $ be the total number of candies Lucy collects after 7 days. **Candy Collection Pattern:** - On Day 1, Lucy collects 10 candies. - Each subsequent day, she collects 2 more candies than the previous day. **Number of Candies Collected Each Day:** - Day 1: 10 candies - Day 2: $ 10 + 2 = 12 $ candies - Day 3: $ 12 + 2 = 14 $ candies - Day 4: $ 14 + 2 = 16 $ candies - Day 5: $ 16 + 2 = 18 $ candies - Day 6: $ 18 + 2 = 20 $ candies - Day 7: $ 20 + 2 = 22 $ candies **Total Candies Collected Over 7 Days:** To find $ C $: $$ C = 10 + 12 + 14 + 16 + 18 + 20 + 22 $$ **Calculating:** $$ C = 10 + 12 + 14 + 16 + 18 + 20 + 22 = 10 + (12 + 14 + 16 + 18 + 20 + 22) $$ $$ C = 10 + (12 + 22) + (14 + 20) + (16 + 18) $$ $$ C = 10 + 34 + 34 + 34 $$ $$ C = 10 + 102 = 112 $$ **Final Solution:** Lucy will have collected a total of **112 candies** after 7 days.