Would anyone be so kind as to check my answers BEFORE I go over the problems with my child? For some of you math geniuses, these are probably simple, but for someone who is not good @ math, but trying to learn! it can be quite painful. Thanks for reading!

1. Mrs Jones is between 50 and 80 yrs. If you divide her age by 9, the remainder is 1. If you divide her age by 4, the remainder is 1. How old is Mrs. Jones?
ANSWER = I couldn't get this one, as I thought the answer might be 64 if she was 63 but then 16 x 4 = 64 & there's no remainder. 73 was another choice but then it doesn't work with the dividing by 4 again as there's no remainder.

2. Jon counts 50 cars that pass his house. One-fifth of the cars contain more than one person. Of the cars containing only one person, three-fifths are driven by women. Of the cars containing just one person, how many cars are driven by men? ANSWER = ONE FIFTH?

3. What is the smallest prime number that is a divisor of the following after all the arithmetic is completed (13 x 17) + (19 x 23).
ANSWER = When I added the two I got 658. Would 2 be the smallest prime number then?

4. One natural number is 4 times as great as a second natural number. Thr product of the two numbers is 36. What is the sum of two numbers?
ANSWER - I thought it might be 4 and 9 and thus the sum would be 13?

If you have gotten this far, thanks for reading!

2. Hello,
Originally Posted by fecoupefe
1. Mrs Jones is between 50 and 80 yrs. If you divide her age by 9, the remainder is 1. If you divide her age by 4, the remainder is 1. How old is Mrs. Jones?
ANSWER = I couldn't get this one, as I thought the answer might be 64 if she was 63 but then 16 x 4 = 64 & there's no remainder. 73 was another choice but then it doesn't work with the dividing by 4 again as there's no remainder.
Well $73=72+1=4\times 18+1$ so if you divide 73 by 4 the remainder is 1... it does work.

2. Jon counts 50 cars that pass his house. One-fifth of the cars contain more than one person. Of the cars containing only one person, three-fifths are driven by women. Of the cars containing just one person, how many cars are driven by men? ANSWER = ONE FIFTH?
One fifth of the cars contain more than one person so five fifth - one fifth = four fifth of the cars contain one person or less than one person. As there is a driver in every car (I guess ), there is no car that contains less than one person. Hence four fifth of the cars contains exactly one person. That is to say $\frac45\times 50 = 40$ cars contain one person.

Now we are told that two fifth of these cars are driven by women. This means that five fifth - two fifth = three fifth of the cars are driven by men. So the number of cars containing one person and driven by men is $\frac35\times40=24$.
3. What is the smallest prime number that is a divisor of the following after all the arithmetic is completed (13 x 17) + (19 x 23).
ANSWER = When I added the two I got 658. Would 2 be the smallest prime number then?
Yes. Another way to get the answer is to see that 13 and 17 are odd numbers so $13\times17$ is odd two. Similarly, $19\times23$ is odd because both 19 and 23 are odd. As the sum of two odd numbers is an even number, $(13 \times 17) + (19 \times 23)$ is even and thus divisible by 2.
4. One natural number is 4 times as great as a second natural number. Thr product of the two numbers is 36. What is the sum of two numbers?
ANSWER - I thought it might be 4 and 9 and thus the sum would be 13?
But 9 is not 4 times as great as 4...

Hello fecoupefe
Originally Posted by fecoupefe
2. Jon counts 50 cars that pass his house. One-fifth of the cars contain more than one person. Of the cars containing only one person, three-fifths are driven by women. Of the cars containing just one person, how many cars are driven by men? ANSWER = ONE FIFTH?
Four-fifths of 50 = 40 = number of cars containing only one person. Of these two-fifths are driven by men. So the number driven by men = $\frac{2}{5}\times 40 = 16$.

Originally Posted by fecoupefe
4. One natural number is 4 times as great as a second natural number. Thr product of the two numbers is 36. What is the sum of two numbers?
ANSWER - I thought it might be 4 and 9 and thus the sum would be 13?
If you understand it, the easiest way is to use algebra, like this:

Suppose that the smaller number is $x$. Then the larger number is $4 \times x = 4x$. The product of $x$ and $4x$ is $x \times 4x = 4x \times x = 4x^2$, and this is equal to $36$. So

$4x^2 = 36$

Divide both sides by $4$:

$x^2 = 9$

Now x is a natural (counting) number, so $x = 3$. So the numbers are 3 and 12, and their sum is 15.

But for someone who hasn't done this sort of algebra, the easiest alternative is probably to use trial and error. So, guess a number that seems about right for the smaller number; say 5. 4 x 5 = 20, and 20 x 5 = 100. That's much too big.

So, now try, say, 2. 2 x 4 = 8, and 8 x 2 = 16. Too small.

Guess 3. 3 x 4 = 12 and 12 x 3 = 36. Correct!

I hope this helps.

Four-fifths of 50 = 40 = number of cars containing only one person. Of these two-fifths are driven by men. So the number driven by men = $\frac{2}{5}\times 40 = 16$.