Patterned Piggy Bank

Maya starts saving money in her piggy bank on March 1st.

She follows this pattern:

  • Every day, she puts a dime in the bank.
  • Every third day, starting on March 3rd, she also puts a quarter in the bank.
  • Every fourth day, starting on March 4th, she also puts a loonie in the bank.

In Canada, a dime is worth 10 cents, a quarter is worth 25 cents, and a loonie is worth one dollar (100 cents).

๐Ÿท Patterned Piggy Bank Tracking Maya's Coins! $1 The Coin Rules: 10ยข Dime: EVERY DAY (1, 2, 3...) 25ยข Quarter: EVERY 3rd DAY (3, 6, 9...) $1 Loonie: EVERY 4th DAY (4, 8, 12...) March Calendar Pattern Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10 Day 11 Day 12! ...and the pattern repeats!

Questions

(a) How many coins does Maya add to her piggy bank on March 12th?

(b) How many coins does Maya add to her piggy bank on March 15th?

(c) How many coins in total does Maya have in her piggy bank by the end of March 16th?

(d) If Maya keeps saving this way, how much money will she have after 20 days?

Solution

(a) On March 12th (Day 12), Maya adds 3 coins to her piggy bank (1 dime, 1 quarter, and 1 loonie).

(b) On March 15th (Day 15), Maya adds 2 coins to her piggy bank (1 dime and 1 quarter).

(c) By the end of March 16th, Maya will have added coins for 16 days. The pattern repeats every 12 days, so we can calculate:
– 12 days: $5.20
– 4 more days: $0.10 + $1.10 + $0.35 + $0.10 = $1.65
Total: $5.20 + $1.65 = $6.85

Total coins: 19 (from 12 days) + 5 (from 4 days) = 24 coins

(d) After 20 days:
– 12 days: $5.20
– 8 more days: $1.65 + $0.10 + $0.35 + $1.10 + $0.10 = $3.30
Total: $5.20 + $3.30 = $8.50

Therefore, after 20 days, Maya will have $8.50 in her piggy bank.

๐Ÿท Piggy Bank Ledger Day Coins Added Total $ 1 10 $0.10 2 10 $0.20 3 10 25 $0.55 4 10 $1 $1.65 5 10 $1.75 6 10 25 $2.10 7 10 $2.20 8 10 $1 $3.30 9 10 25 $3.65 10 10 $3.75 11 10 $3.85 12! 10 25 $1 $5.20 Final Answers (a) Mar 12th Maya adds: 3 Coins (b) Mar 15th Maya adds: 2 Coins (c) End of Mar 16th (16 Days) Cycle ($5.20) + 4 days ($1.65) Total Money: $6.85 (25 Coins) (d) After 20 Days Cycle ($5.20) + 8 days ($3.30) Total Money: $8.50