If you divide a certain number by 17, the quotient is 47 and the remainder is 2. What is the number?
What is the sum if all the numbers less than 496 that divides evenly into 496?
The ratio of girls to boys in a class is 3:2m. If there are 35 students in the class, how many are boys?
Also, all of these question are from the Spirit of Math grade 6 mastermind assignment. I have also noticed that a lot of the questions on this website is from Spirit of Math. Last thing I noticed is that most of the questions on this website are from 2014 and the answer that are actual right are from the same day on the same year ( 2014)
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To find the number when divided by 17, the quotient is 47, and the remainder is 2, you can use basic algebraic equations. Let's denote the number as x.
1. The first equation would be x = 17 * 47 + 2 since the quotient multiplied by the divisor (17) plus the remainder (2) gives the actual number.
Now, let's solve for x:
x = 17 * 47 + 2
x = 799 + 2
x = 801
Therefore, the number is 801.
To find the sum of all the numbers less than 496 that divide evenly into 496, we can use a loop or a formula.
2. With a loop:
Start with a variable called "sum" set to 0. Then, iterate through all numbers less than 496 (i.e., from 1 to 495) and check if they divide evenly into 496. When a number does divide evenly, add it to the "sum" variable. Finally, the sum will contain the total sum of all the numbers.
Here's an example in Python code:
sum = 0
for i in range(1, 496):
if 496 % i == 0:
sum += i
The value of "sum" will be the answer.
Alternatively, you can use a formula to calculate the sum of the divisors of a number. For a number n, the sum of its divisors can be found using the formula:
sum = (p1^(a1+1) - 1) / (p1 - 1) * (p2^(a2+1) - 1) / (p2 - 1) * ...
Where p1, p2, etc. are prime factors of n, and a1, a2, etc. are their corresponding exponents.
For 496, its prime factorization is 2^4 * 31^1.
Substituting these values into the formula:
sum = (2^(4+1) - 1) / (2 - 1) * (31^(1+1) - 1) / (31 - 1)
sum = (32 - 1) / 1 * (961 - 1) / 30
sum = 31 * 960 / 30
sum = 992
Therefore, the sum of all numbers less than 496 that divide evenly into 496 is 992.
For the third question about the ratio of girls to boys in a class, we are given that the ratio is 3:2m, where m represents an unknown multiplier. We are also given that there are 35 students in the class.
3. To find the number of boys in the class, we need to determine the value of m.
The ratio of girls to boys is 3:2m, where the total ratio is 3 + 2m.
Since there are 35 students in total, we can set up an equation:
3 + 2m = 35
Now, solve for m:
2m = 35 - 3
2m = 32
m = 16
With m equal to 16, we can find the number of boys by substituting the value of m into the ratio equation:
2m = 2 * 16 = 32
Therefore, there are 32 boys in the class.