Answer :
To determine the total number of coins in Bard's collection after 4 months, we can follow these steps:
1. Initial Amount: Bard starts with 42 coins in his collection.
2. Coins Bought Each Month: Bard buys 3 more coins each month.
3. Time Frame: We need to calculate the number of coins after 4 months.
4. Calculate Coins Added:
- Each month, Bard buys 3 coins.
- Over 4 months, the number of coins Bard buys is [tex]\(3 \times 4 = 12\)[/tex].
5. Total Coins After 4 Months:
- Add the initial number of coins (42) to the coins added over 4 months (12).
- So, [tex]\(42 + 12 = 54\)[/tex].
6. Review the Expressions: Now let's analyze the given expressions to see which ones match this calculation:
- [tex]\(42 + 12\)[/tex]: Correct, as this directly calculates the total number of coins after 4 months.
- [tex]\(42 \times 3 \times 4\)[/tex]: Incorrect, because it multiplies coins instead of adding the monthly coins.
- [tex]\(42 + 3 \times 4\)[/tex]: Correct, as it also results in the correct total by considering 3 coins each for 4 months.
- [tex]\(42 + 3 + 4\)[/tex]: Incorrect, because it simply adds 3 and 4 to 42 without considering the proper multiplication of monthly coins.
- [tex]\(42 \times 3 \times 3 \times 3 \times 3\)[/tex]: Incorrect, since it multiplies 42 by 3 four times, which doesn’t align with the monthly addition process.
- [tex]\(=2 + 3 + 3 + 3 + 3\)[/tex]: Incorrect, because it doesn't reflect the proper calculation or initial coin count.
Thus, the expressions [tex]\(42 + 12\)[/tex] and [tex]\(42 + 3 \times 4\)[/tex] correctly represent the total number of coins in Bard's collection after 4 months, which is 54 coins.
1. Initial Amount: Bard starts with 42 coins in his collection.
2. Coins Bought Each Month: Bard buys 3 more coins each month.
3. Time Frame: We need to calculate the number of coins after 4 months.
4. Calculate Coins Added:
- Each month, Bard buys 3 coins.
- Over 4 months, the number of coins Bard buys is [tex]\(3 \times 4 = 12\)[/tex].
5. Total Coins After 4 Months:
- Add the initial number of coins (42) to the coins added over 4 months (12).
- So, [tex]\(42 + 12 = 54\)[/tex].
6. Review the Expressions: Now let's analyze the given expressions to see which ones match this calculation:
- [tex]\(42 + 12\)[/tex]: Correct, as this directly calculates the total number of coins after 4 months.
- [tex]\(42 \times 3 \times 4\)[/tex]: Incorrect, because it multiplies coins instead of adding the monthly coins.
- [tex]\(42 + 3 \times 4\)[/tex]: Correct, as it also results in the correct total by considering 3 coins each for 4 months.
- [tex]\(42 + 3 + 4\)[/tex]: Incorrect, because it simply adds 3 and 4 to 42 without considering the proper multiplication of monthly coins.
- [tex]\(42 \times 3 \times 3 \times 3 \times 3\)[/tex]: Incorrect, since it multiplies 42 by 3 four times, which doesn’t align with the monthly addition process.
- [tex]\(=2 + 3 + 3 + 3 + 3\)[/tex]: Incorrect, because it doesn't reflect the proper calculation or initial coin count.
Thus, the expressions [tex]\(42 + 12\)[/tex] and [tex]\(42 + 3 \times 4\)[/tex] correctly represent the total number of coins in Bard's collection after 4 months, which is 54 coins.
