SAT Tip of the Week: Ratios
In general, the problems on the SAT involving ratios and proportions are some of the
easiest problems you will see on the test. However, there is a “trick”. You need to keep
track of the units. If you do this, you’ll be golden. When you see a problem and you
know it is a ratio problem, you should set up the problem by first writing the units. Yes,
actually write them. Then, when you put in the numbers, put them in the same order
that you wrote the units in.
Example #1: A certain farm raises 2 kinds of animals: horses and ducks. The ratio of
horses to ducks is 2 to 7. If there are 63 animals on the farm, how many are horses?
A) 13 B) 14 C) 16 D) 18 E) 49
2
x
and you’ll choose (D). But

7 63
horses
this is not the correct answer. The ratio on the left has units of
and the ratio on
ducks
horses
the right has units of
. If you set them equal, you don’t have matching
total# animals
If you aren’t careful about your units, you’ll do this:
units. Instead, you need to remember that if you have a ratio of 2 horses to 7 ducks,
that means out of 9 animals. So the correct proportion is
horses
2
x
and
: 
total# animals 9 63
now you’ll get the correct answer of (B).
That’s the main “trick”. However, sometimes they’ll try one more trick, and that is to
cause you to need to change the units.
There is another type of ratio problem that you may encounter, and that is with similar
figures. Recall that 2 polygons are similar when their corresponding angles are
congruent and their corresponding sides are proportional. (all circles are similar to
each other)
Example #2: Given 2 circles A and B. If the ratio of the diameter of circle A to the
diameter of circle B is 5:3, what is the ratio of the area of circle A to the area of circle B?
Answer: 25:9 since the area is πr2 and the radii are also proportional to 5:3.
SAT Tip of the Week: Ratios
Due _________
Directions: For each problem, you must show your work or explain your answer for full credit.
Remember, calculators are allowed on the entire SAT Math test. You must use a pencil.
1. In Mrs. Michel’s Honors Precalculus class,
the ratio of boys to girls is 7 to 5. If there
are 14 boys in the class, how many
students are in the class?
A. 10
B. 20
C. 24
D. 25
E. 36
2. A recipe for making 10 cakes requires 24 cups
of flour and 4 tablespoons of baking powder.
Janet wants to only make 3 cakes. How
many cups of flour will she need? (do not
round your answer)
A. 2.7
B. 3
C. 7
D. 7.2
E. 9
3. The ratio of 1.5 to 32 is the same as the
ratio of 0.15 to x. What is the value of x?
4. A bag contains marbles that are either solid
or striped. The ratio of solid to striped
marbles is 4 to 3. When 5 solid and 5 striped
marbles are removed from the bag, the new
ratio is 3 to 2. How many solid marbles were
originally in the bag?
A. 12
B. 15
C. 18
D. 20
E. 30
5. Given 2 circles A and B. If the ratio of
the circumference of circle A to the
circumference of circle B is 4:3, what
is the ratio of the area of circle A to
the area of circle B?
6. Given 2 similar triangles with sides of 5 and 2
as shown. If the area of XYZ is 30, what is
the area of ABC?
SAT Tip of the Week: Ratios
ANSWER KEY
Directions: For each problem, you must show your work or explain your answer for full credit.
Remember, calculators are allowed on the entire SAT Math test. You must use a pencil.
1. In Mrs. Michel’s Honors Precalculus class,
the ratio of boys to girls is 7 to 5. If there
are 14 boys in the class, how many
students are in the class? C. 24
boys 7 14
:

total 12
x
3. The ratio of 1.5 to 32 is the same as the
ratio of 0.15 to x. What is the value of x?
x is 3.2
1.5 0.15

32
x
5. Given 2 circles A and B. If the ratio of
the circumference of circle A to the
circumference of circle B is 4:3, what
is the ratio of the area of circle A to
the area of circle B?
42:32 or 16:9
2. A recipe for making 10 cakes requires 24 cups
of flour and 4 tablespoons of baking powder.
Janet wants to only make 3 cakes. How
many cups of flour will she need? (do not
round your answer) D. 7.2
cups flour 24 x
:

# cakes 10 3
4. A bag contains marbles that are either solid
or striped. The ratio of solid to striped
marbles is 4 to 3. When 5 solid and 5 striped
marbles are removed from the bag, the new
ratio is 3 to 2. How many solid marbles were
originally in the bag? There were 20 solid
marbles
# solid 4 4 x
; take out 5 of each and
: 
# striped 3 3 x
# solid 4 x  5 3
get
:
 and solve for x.
# striped 3 x  5 2
Now plug x back in. There were originally 4x
solid marbles, so there were 4(5)=20
6. Given 2 similar triangles with sides of 5 and 2
as shown. If the area of XYZ is 30, what is
the area of ABC?
24/5 or 4.8
Find the height of XYZ. ½ bh=30, so h = 12.
XYZ 12 5
:
 ; so h=24/5. Find the A and
ABC h 2
it is also 24/5.
Or, we know the height is also proportional to
5:2. The area is ½ bh and so it is 52:22. So
area is:
XYZ 30 25
and A=24/5
:

ABC A
4