Andrew is making a plan to complete a class math assignment. He has 48 problems to complete over 5 days. He decides to complete the assignment is such a way that his total number of completed problems doubles every day. He realizes that that number must be 48 by the end of the fifth day.
How many problems does Andrew need to solve on the first day?
Please help me, thanks!
3, 6, 12, 24, 48
To find out how many problems Andrew needs to solve on the first day, we can work backwards from the total number of problems he wants to complete by the end of the fifth day.
Since his total number of problems doubles every day, he must solve half the number of problems he needs to solve on the second day on the first day.
Let's denote the number of problems he needs to solve on the first day as "x".
On the second day, he would need to solve twice the number of problems he solved on the first day, which is 2x.
On the third day, he would need to solve twice the number of problems he solved on the second day, which is 2 * (2x) = 4x.
On the fourth day, he would need to solve twice the number of problems he solved on the third day, which is 2 * (4x) = 8x.
On the fifth day, he would need to solve twice the number of problems he solved on the fourth day, which is 2 * (8x) = 16x.
We know that the total number of problems he wants to complete by the end of the fifth day is 48. So we can set up an equation:
x + 2x + 4x + 8x + 16x = 48
To solve this equation, we can simplify it:
31x = 48
Now we solve for x:
x = 48 / 31
Calculating this, we find that:
x ≈ 1.548
Since Andrew can't solve a fractional number of problems, he should solve 2 problems on the first day to ensure that his total number of completed problems doubles each day and reaches 48 by the end of the fifth day.