In June, Cory beings to save money for a video game and a TV he wants to buy in December. He starts with $22. Each month he plans to save 10% more than the previous month. How much money will he have at the end of December?
To solve this problem, we can start by calculating how much Cory will save each month:
- In June, he saves 10% of $22, which is $2.20. So he now has $24.20.
- In July, he saves 10% more than in June, which is 10% of $24.20 (or $2.42). So he now has $26.62.
- In August, he saves 10% more than in July, which is 10% of $26.62 (or $2.66). So he now has $29.28.
- And so on, until December.
We can use a table to keep track of how much he saves each month:
| Month | Starting amount | Percentage | Amount saved | Ending amount |
|-------|----------------|------------|--------------|---------------|
| June | $22.00 | 10% | $2.20 | $24.20 |
| July | $24.20 | 20% | $2.42 | $26.62 |
| August | $26.62 | 30% | $2.66 | $29.28 |
| September | $29.28 | 40% | $2.93 | $32.21 |
| October | $32.21 | 50% | $3.22 | $35.43 |
| November | $35.43 | 60% | $3.54 | $39.97 |
| December | $39.97 | 70% | $4.00 | $43.97 |
So at the end of December, Cory will have $43.97 saved up.
are you sure
Yes, I'm sure. Here's the calculation to show how we arrived at this amount:
- Start with $22 in June.
- In June, he saves $2.20, so he has $24.20 in July.
- In July, he saves $2.42, so he has $26.62 in August.
- In August, he saves $2.66, so he has $29.28 in September.
- In September, he saves $2.93, so he has $32.21 in October.
- In October, he saves $3.22, so he has $35.43 in November.
- In November, he saves $3.54, so he has $39.97 in December.
- In December, he saves $4.00, so his final total is $43.97.
Therefore, Cory will have $43.97 saved up at the end of December.
To calculate how much money Cory will have at the end of December, we first need to determine his savings for each month leading up to December.
Let's calculate his savings step-by-step:
1. In June, Cory starts with $22.
2. In July, he plans to save 10% more than in June.
Savings in July = $22 + 10% of $22
= $22 + (10/100) x $22
= $22 + $2.20
= $24.20
3. In August, he plans to save 10% more than in July.
Savings in August = $24.20 + 10% of $24.20
= $24.20 + (10/100) x $24.20
= $24.20 + $2.42
= $26.62
4. We continue this pattern for the remaining months, increasing the savings by 10% each time.
Calculating the savings for the remaining months using the same method:
September: $26.62 + 10% of $26.62 = $26.62 + $2.66 = $29.28
October: $29.28 + 10% of $29.28 = $29.28 + $2.93 = $32.21
November: $32.21 + 10% of $32.21 = $32.21 + $3.22 = $35.43
December: $35.43 + 10% of $35.43 = $35.43 + $3.54 = $38.97
Therefore, at the end of December, Cory will have $38.97.