We have here a basic ratio:

6/24 = 57/x

Solving for x, we get: 6x = 24 * 57; 6x = 1368; x = 228

Now, we must be very careful here, however. Is 228 an even multiple of 24?  228/24 = 9.5.  That means that we would have to do 9.5 batches.  The question indicates that these are batched in groups of 6; therefore, we have to run 10 batches to get our amount. That would be 240 minutes or 4 hours.

Set up a proportion and conver 4 hours and 20 minutes into just minutes for now,

so 26/260 = 100/X

Solve for X = 1000 minutes

1000/60 = 16 hours and 40 minutes

We can set up a ratio of \(\displaystyle \frac{3}{x}=\frac{6}{12}\) and then solve for \(\displaystyle x\). 

The weight will be 150 grams + (1.15 – 0.55)/0.05 * 50g.

You need to subtract first 150 grams cost from the total cost and divide by the price per unit to determine how many units. Next, multiply units by weight per unit and add to the original first 150 grams.

 150 + 600 = 750 grams

This is the maximum weight that can be sent at that price; the minimum weight that could be charged this price would be 701 grams. Hence a package weighing 750 grams will be charged $1.15.

Let us express this as an algebraic expression:

\(\displaystyle \frac{6}{13.5}=\frac{17}{x}\)

We can cross multiply:

\(\displaystyle 6x=13.5\times 17\)

\(\displaystyle 6x=229.5\)

\(\displaystyle x=\frac{229.5}{6}=38.25\)

Once you subtract the 5 students that don't own either, there are 80 students left.

There's 96 total students when you add the number that own an mp3 and the number that own a laptop, meaning 16 own both.

Recall that the fraction will be number of students who have both laptop and mp3 divided by the total students in the class.

\(\displaystyle =\frac{16}{85}\)

a ratio that comes from a fraction is the numerator: denominator

7/8 = 7:8

1m 40cm = 140cm. 1m = 100cm. So the ratio is 140cm:100cm. This can be put as a fraction 140/100 and then reduced to 14/10 and further to 7/5. This, in turn, can be rewritten as a ratio as 7:5.

One remote is defective for every 199 non-defective remotes.

Begin by making your life easier: presume that there are \(\displaystyle 6\) papers on the desk. Immediately, we know that there are \(\displaystyle 2\) paper clips. Now, if there are \(\displaystyle 6\) papers, you know that there also must be \(\displaystyle 2\) greeting cards. Technically you figure this out by using the ratio:

\(\displaystyle \frac{3}{1}=\frac{6}{x}\)

By cross-multiplying you get:

\(\displaystyle 3x=6\)

Solving for \(\displaystyle x\), you clearly get \(\displaystyle x=2\).

(Many students will likely see this fact without doing the algebra, however. The numbers are rather simple.)

Now, this means that our desk has on it:

\(\displaystyle 6\) papers

\(\displaystyle 2\) paper clips

\(\displaystyle 2\) greeting cards

Therefore, you have \(\displaystyle 10\) total items.  Based on this, your ratio of paper clips to total items is:

\(\displaystyle \frac{2}{10}=\frac{1}{5}\), which is the same as \(\displaystyle 1:5\).