1) During the two months of the summer holiday, you find a summer job that pays $160 per week with a $10 a week raise. How much money will be made by the end of the summer?
2 Your grandmother offers you $1 on the first day of March break and offers to double it each day of the break to help her with chores in her house. If you were to help her for 7 days over the break, how much money would you get at the end of day 7?
One way to solve these problems is the long way.
1.
160
170
180
190
Continue until you reach 8 weeks.
Add these numbers together to find the total.
2.
1
2
4
8
16
32
64
To find the answer to the first question, we need to calculate how much money will be made each week during the summer holiday and then sum up the total for 8 weeks.
1) The summer job pays $160 per week with a $10 raise each week. We can calculate the total earnings using the following formula:
Total Earnings = (Initial Pay + Raise per week) * Number of weeks
Since the initial pay is $160 and the raise per week is $10, the formula becomes:
Total Earnings = ($160 + $10) * 8
Calculating this equation, we get:
Total Earnings = $170 * 8
Total Earnings = $1360
Therefore, by the end of the summer, $1360 will be made.
Now, let's move on to the second question.
2) Your grandmother offers you $1 on the first day of March break and doubles the amount each day for seven days.
To calculate the total money received at the end of day 7, we can use the formula for calculating geometric progression:
Total Money = Initial Amount * (1 - r^n) / (1 - r)
Where:
Initial Amount = $1 (the amount offered on the first day)
r = 2 (doubling factor)
n = 7 (number of days)
Applying these values to the formula, we have:
Total Money = $1 * (1 - 2^7) / (1 - 2)
Simplifying the equation, we get:
Total Money = $1 * (1 - 128) / (1 - 2)
Total Money = -$127 / -1
Total Money = $127
Therefore, at the end of day 7, you would receive $127.