**#1: At a county fair, if adults to kids ratio is 2 to 3 and there are 250 people at the fair. How many adults and how many kids?**

Solution I : Adults to Kids = 2 : 3 (given). Let there be 2x adults and 3x kids (only when two numbers have the same multiples can you simplify the two number to relatively prime.

2x + 3x = 250; 5x = 250; x = 50 so there are 2x or 2 * 50 = 100 adults and 3x or 3 * 50 = 150 kids.

Solution II: From the given information, you know that every time when there are 5 parts (2 + 3 = 5), there

will be 2 parts for A, or of the total, and 3 parts for B, or of the total.

* 250 = 100 adults and * 250 = 150 kids

**#2: In a mixture of peanuts and cashews, the ratio by weight of peanuts to cashews is 5 to 2. How many pounds of cashews will there be in 4 pounds of this mixture? (an actual SAT question)**

Solution:

You can

**use either the first or second method (see above two solutions) but the second solution is much faster.**

* 4 = pounds

**#3: Continue with question #1: How many more kids than adults go to the fair?**

Solution I:

Use the method on #1 and then find the difference.

150 - 100 =

**50 more kids.**

Solution II:

Using the method for #1: solution II, you know of the all the people go to the fair are adults ,

and of the total people go to the fair are kids.

( - ) * 250 =

**50 more kids**.

**#3: If the girls to boys ratio at an elementary school is 3 to 4 and there are 123 girls, how many boys are there at that elementary school?**

Solution:

This one is easy, you set up the equation. Just make sure the numbers line up nicely.

Let there be "

*x*" boys. = . Cross multiply to get x. Or since 123 is 41 * 3;

4 * 41 =

**164 boys**

**#4 :**

**If the girls to boys ratio at an elementary school is 2 to 5 and there are 78 more boys than girls, how many girls are there at the elementary school?**

Solution I:

Again, you can use the algebra and let there be 2x girls and 5x boys.

According to the given, 5x - 2x = 3x = 78 so x = 26

Plug in and you get there are 2*26 =

**52 girls**and 5*26 = 130 boys.

Solution II:

If you keep expanding the ratio using the same multiples, 2 : 5 = 4 : 10 : 6 : 15...

Do you see that the difference of boys and girls are always multiples of 3 ( 5 - 2 = 3).

= 26 so there are 2 * 26 or

**52 girls**