sally and hans started counting at the same time. sally counted on by tens from 300. hans counted back by hundreds. after six counts they had reached the same number. what number did hans start counting from?
Han's starting number ------ x , counts backwards by 100
Sally's starting number ----- 300 counts forward by 10
after 6 counts, Sally is 360
after 6 counts, Han's is at x - 600
x - 600 = 360
x = 960
Well, if Sally counted on by tens from 300, she would have counted 310, 320, and so on. Meanwhile, Hans counted back by hundreds. So, after six counts, he would have counted 600, 500, and so on.
The question says they reached the same number after six counts, so we know that their sixth counts must match.
If Sally's sixth count is 560, that means she counted 10, 20, 30... all the way up to 560.
On the other hand, if Hans' sixth count is also 560, that means he counted 900, 800, 700... all the way down to 560.
So, Hans must have started counting from 900.
Let's break down the information given:
Sally started counting on by tens from 300. This means her counts would be: 300, 310, 320, 330, 340, 350.
Hans counted back by hundreds. Since they reached the same number after six counts, we can deduce that Hans also counted six times.
To find the starting number for Hans, we begin from the same final number as Sally, which is 350, and count back six times by hundreds. Starting from 350 and counting back six times, we get the following sequence: 350, 250, 150, 50, -50, -150.
Therefore, Hans started counting from -150.
To solve this problem, we need to understand the counting pattern of Sally and Hans. Let's break down the information provided:
Sally counted on by tens from 300. This means she counted 310, 320, 330, and so on.
Hans counted back by hundreds. Therefore, he counted 200, 100, 0, -100, and so on.
After six counts, they reached the same number.
Now, let's find the number they both reached:
Sally's counts from 300: 300, 310, 320, 330, 340, 350, 360
Hans' counts starting from an unknown number (let's call it X): X, X - 100, X - 200, X - 300, X - 400, X - 500, X - 600
To find the number they both reached after six counts, we need to find the number that is common to both sequences. Comparing the two patterns, we can see that:
X - 600 = 360
Let's solve for X:
X - 600 = 360
X = 360 + 600
X = 960
Therefore, Hans started counting from 960.