Having trouble with summer word problems. Please help.

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ashley_moonlight

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Okay, so I'm working on my summer math packet, (last minute I know) and I cannot for the life of me remember how to do these problems. Could you please help me? 1: There is a total of 56 _, and the ratio of x to y is 5:3. How many total of x are there? 2: What is equivalent to multiplying any number N, by 2. I know these are simple, but I completely forgot. If you decide to help, don't just answer, help me understand it please, so I'm ready for school starting tomorrow.
 
ashley_moonlight said:
Okay, so I'm working on my summer math packet, (last minute I know) and I cannot for the life of me remember how to do these problems. Could you please help me?

1: There is a total of 56 _, and the ratio of x to y is 5:3. How many total of x are there?

The above does not make sense - please read/edit and repost.

2: What is equivalent to multiplying any number N, by 2.

Another representation of multiplication is addition.

I know these are simple, but I completely forgot. If you decide to help, don't just answer, help me understand it please, so I'm ready for school starting tomorrow.
Click to expand...
 
ashley_moonlight said:
1: There is a total of 56 _, and the ratio of x to y is 5:3. How many total of x are there?
Click to expand...

\(\displaystyle 1.\)

Let \(\displaystyle k\) be a positive integer.

\(\displaystyle \frac{x}{y} = \frac {5}{3}\)

We can state \(\displaystyle \frac{5}{3} = \frac{5k}{3k} = \frac{x}{y}\), for a common factor of \(\displaystyle k.\)

\(\displaystyle x + y = 56\)

So \(\displaystyle 5k + 3k = 56\)

\(\displaystyle 8k = 56\)

\(\displaystyle k = 7\)

But \(\displaystyle x = 5k\), and then you can finish the problem.
 
2. What is equivalent to multiplying any number N, by 2?

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(i) As Subhotosh Khan referred to, you can add \(\displaystyle N\) to itself, as in \(\displaystyle N + N.\)

(ii) You can divide \(\displaystyle N\) by \(\displaystyle \frac{1}{2}\).

(iii) You can divide \(\displaystyle N\) by \(\displaystyle 0.5\)

(iv) You can add \(\displaystyle 100\)% of \(\displaystyle N\) to itself, as in \(\displaystyle N + N(100\)%\(\displaystyle ).\)

This is the same meaning as increasing \(\displaystyle N\) by \(\displaystyle 100\)%.
 
2) . What is equivalent to multiplying any number N, by 2? Assuming N is an integer, then 2N is an even integer.
 
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