We know that Stacy has \(\displaystyle \small 4\) 1946 dimes.

We also know that she has twice as many wheat pennies, so we must multiply \(\displaystyle \small 4\) by \(\displaystyle \small 2\) to find the total number of wheat pennies.

\(\displaystyle \small 4\cdot 2=8\)

We also know that Stacy has three times as many 1986 quarters, so we multiply \(\displaystyle \small 4\) by \(\displaystyle \small 3\) to find the total number of 1986 quarters.

\(\displaystyle \small 4\cdot 3=12\)

Now our ratio of wheat pennies to 1986 quarters is \(\displaystyle \small 8:12\), but this can be simplified because both numbers are divisible by \(\displaystyle \small 4\).

\(\displaystyle \small (8/4)=2\)

\(\displaystyle \small (12/4)=3\)

So our ratio becomes \(\displaystyle \small 2:3\)

Since there are \(\displaystyle \small 27\) customers who order orange juice, \(\displaystyle \small 27\) is the first number of our ratio. 

The second number of our ratio is \(\displaystyle \small 37\), because \(\displaystyle \small 37\) people order coffee. 

Therefore, our ratio is :

\(\displaystyle \small 27:37\)

Counting Steve, there are forty attendees so far, fifteen of whom are girls and twenty-five of whom (including Steve) are boys. To obtain a two-to-one girl to boy ratio, he needs to invite a total of fifty girls, so he needs to invite thirty-five more.

If Scott's mother bakes 12 cookies and he eats half of them, that means he will eat 6 cookies, leaving 6 uneaten cookies.

If Scott's mom then puts red frosting on 4 cookies and blue frosting on the rest of the cookies, 2 cookies will get blue frosting. (\(\displaystyle 4+2=6\)). 

Therefore, the ratio of cookies with red frosting to cookies with blue frosting is \(\displaystyle 4:2\), which is equal to \(\displaystyle 2:1\).

Given that there are 3 peanuts for every 1 chocolate chip and 2 raisins, the proportion of raisins can be found by dividing the number of raisins by the sum of all the items in the mix. This results in:

\(\displaystyle \frac{2}{3+1+2}=\frac{2}{6}=\frac{1}{3}\). 

Therefore, \(\displaystyle \frac{1}{3}\) is the correct answer. 

The ratio of Jose to Michael's height is \(\displaystyle 3:1\).

Thus, if Jose is \(\displaystyle 48\) inches taller than Michael must be \(\displaystyle 3\) times shorter.

We can write this as the expression, \(\displaystyle \frac{48}{3}=16\).

Also, an equivalent ratio for \(\displaystyle 3:1\) = \(\displaystyle 48:16\).

An equivalent ratio of \(\displaystyle 15:3\) is \(\displaystyle 5:1\).

This is the furthest simplification of the ratio. 
The greatest common divisor is needed to simplify the expression.

Both \(\displaystyle 15\) and \(\displaystyle 3\) are divisible by \(\displaystyle 3\), \(\displaystyle \frac{15}{3}=5\)  and  \(\displaystyle \frac{3}{3}=1\).

Thus, the correct answer is \(\displaystyle 5:1\). 

To solve this problem the relationship between the two numbers in the first ratio needs to be established.

Since, \(\displaystyle 27\) is \(\displaystyle 3\) times larger than \(\displaystyle 9\), an equivalent ratio must have the same relationship.

Thus, \(\displaystyle x\) must be \(\displaystyle 3\) times larger than \(\displaystyle 19\), and \(\displaystyle 19\cdot 3=57\) 

Thus, \(\displaystyle 9:27=19:57\)

First, find the number of boys in the class by subtracting the number of girls in the class from the total number of students.

\(\displaystyle \text{Number of boys}=36-12=24\)

Now, we know that the ratio of the number of boys in the class to the total number of students in the class is \(\displaystyle 24\text{ to }36\).

We can express that ratio as the following fraction:

\(\displaystyle \frac{24}{36}=\frac{2}{3}\)

First, find the number of girls in the class by subtracting the number of boys in the class from the total number of students.

\(\displaystyle \text{Number of girls}=40-15=25\)

Now, we know that the ratio of the number of boys in the class to the total number of students in the class is \(\displaystyle 25\text{ to }40\).

We can express that ratio as the following fraction:

\(\displaystyle \frac{25}{40}=\frac{5}{8}\)