This question is simply asking which number is divisible by 3, 4 and 6 with none left over. The only number that has 3, 4, and 6 as factors is 24.

If \(\displaystyle \frac{1}{4}\) of a pound of candy costs $4 then the price of a full pound will be 4 times as much.  Thus 4 times $4 is $16.  

Let \(\displaystyle N\) be the number desired. The question can be rewritten as the multiplication statement:

\(\displaystyle \frac{2}{5} \cdot N = 500\)

Solve:

\(\displaystyle \frac{5} {2}\cdot \frac{2}{5} \cdot N =\frac{5} {2}\cdot 500\)

\(\displaystyle N =\frac{2,500} {2}=1,250\)

A number is divisible by 9 without a remainder when each of its digits add up to a number that is divisble by 9. When looking at the number 711, we can see that:

\(\displaystyle 7+1+1=9\)

Given that 9 is divisble by 9, (equlaing 1, no remainder), 711 is divisble by 9. 

If Bernard bakes 8 cookies, that means he has used one-sixth of the cookie dough because 48 divided by 8 equals 6. Thus, 8 is one-sixth of 48. 

Therefore, he would have used one-sixth of the dough, or the equivalent of 1 pound. 

This would leave 5 pounds of dough remaining. 

In a rectangle, each corner is equal to 90 degrees. All corners are of equal degrees. Thus, the sum of any three corners would equal the product of 90 and 3, which is 270. Therefore, the correct answer is 270 degrees. 

For this question we look at the multiples of each group and find the smallest factor that is common to all three groups.

Captain Hook: \(\displaystyle 9, 18, 27, \bold{36}, 45, 54\)

Captain Jack: \(\displaystyle 6, 12, 18, 24, 30, \bold{36}\)

Captain James: \(\displaystyle 4, 8, 12, 16, 20, 24, 28, 32, \bold{36}\)

Therefore, the smallest number that is divisible by \(\displaystyle 9, 6,\) and \(\displaystyle 4\) is \(\displaystyle 36\).

If \(\displaystyle x\) is the price per pound, then the formula for this equation is \(\displaystyle \frac{2}{3}x=6\)

Isolate \(\displaystyle x\) by multiplying the inverse of \(\displaystyle \frac{2}{3}\), which is \(\displaystyle \frac{3}{2}\), to both sides.

\(\displaystyle \frac{2}{3}x\bigg(\frac{3}{2}\bigg)=6\bigg(\frac{3}{2}\bigg)\)

\(\displaystyle x=9\)

If \(\displaystyle x\) is the price per acre, then the formula for this equation is \(\displaystyle \frac{1}{8}x=20,000\)

Isolate \(\displaystyle x\) by multiplying the inverse of \(\displaystyle \frac{1}{8}\), which is \(\displaystyle \frac{8}{1}\), to both sides.

\(\displaystyle \frac{1}{8}x\bigg(\frac{8}{1}\bigg)=20,000\bigg(\frac{8}{1}\bigg)\)

\(\displaystyle x=160,000\)

If \(\displaystyle N\) be the number desired. The question can be rewritten as the multiplication statement:

\(\displaystyle \frac{2}{3}N=400\)

Solve:

\(\displaystyle \bigg(\frac{3}{2}\bigg)\frac{2}{3}N=\bigg(\frac{3}{2}\bigg)400\)

\(\displaystyle N=\frac{1200}{2}=600\)