<span>Ayesha's right. There's a good trick for knowing if a number is a multiple of nine called "casting out nines." We just add up the digits, then add up the digits of the sum, and so on. If the result is nine the original number is a multiple of nine. We can stop early if we recognize if a number along the way is or isn't a multiple of nine. The same trick works with multiples of three; we have one if we end with 3, 6 or 9.
So </span>
<span>has a sum of digits 31 whose sum of digits is 4, so this isn't a multiple of nine. It will give a remainder of 4 when divided by 9; let's check.
</span>
<span>
</span>Let's focus on remainders when we divide by nine. The digit summing works because 1 and 10 have the same remainder when divided by nine, namely 1. So we see multiplying by 10 doesn't change the remainder. So
has the same remainder as
.
When Ayesha reverses the digits she doesn't change the sum of the digits, so she doesn't change the remainder. Since the two numbers have the same remainder, when we subtract them we'll get a number whose remainder is the difference, namely zero. That's why her method works.
<span>
It doesn't matter if the digits are larger or smaller or how many there are. We might want the first number bigger than the second so we get a positive difference, but even that doesn't matter; a negative difference will still be a multiple of nine. Let's pick a random number, reverse its digits, subtract, and check it's a multiple of nine:
</span>
Answer: 2075
Step-by-step explanation:
Sonia traveled 2905 miles in 7 days
2905/7=415 miles/day
415*5=2075 miles
Assuming that the number you are attempting to write is 5 8/5, you're whole number would be 6 3/5.
However, if the number is actually 58/5, then the whole number would be 11 3/5.
Here's how to find the answer:
For 5 8/5, you must find how many times 5 goes into the numerator since 5/5 is one whole number. However, there will sometimes be remainders as presented in this question, thus leaving you with another fraction which is 3/5.
Hope this helps!
Answer:
The minimum number of bicycles that must be produced and sold to break even = 20
Explanation:
The profit generated by producing and selling n bicycles per week is given by the formula:
To get the minimum number of bicycles that must be produced and sold to break even, let P(n) = 0 (Since break even means no profit is made)
Solve the resulting quadratic equation above
This means that, to break even, either 60 or 20 bicycles must be produced and sold
The minimum number of bicycles that must be produced and sold to break even = 20