Sat math Essentials

What number i
s
 80% of 40?
x
40
80
100
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Now solve:
0
1
.
0
2
0
5
x
16
0
1
.2
0
5
0
x
16
0
1
.2
0
5
0
x
100 
16 
100
0.25
x
1,600
0.
x
25
1
0
,6
.2
0
5
0
x
6,400
Answer: 0.25% of 6,400 is 16.
■
finding what percentage one number is of another number 
Example
What percentage of 90 is 18?
First translate the problem into math:
Now solve:
10
x
0
90 
18
1
9
0
0
0
x
18
1
9
0
x
18
1
9
0
x
10 
18 
10
9
x
180
x
20
Answer: 18 is 20% of 90.
W
hat precentage of 90 is 18?
x
100
18
90
0.25% of what number is 16?
x
16
0.25
100
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Practice Question
If
z
is 2% of 85, what is 2% of
z
?
a.
0.034
b.
0.34
c.
1.7
d.
3.4
e.
17
Answer
a.
To solve, break the problem into pieces. The first part says that 
z
is 2% of 85. Let’s translate:
Now let’s solve for 
z
:
z
1
2
00
85
z
5
1
0
85
z
8
5
5
0
z
1
1
7
0
Now we know that 
z
1
1
7
0
. The second part asks: What is 2% of
z
? Let’s translate:
Now let’s solve for 
x
when 
z
1
1
7
0
.
x
1
2
00
z
Plug in the value of
z.
x
1
2
00
1
1
7
0
x
1,
3
0
4
00
0.034
Therefore, 0.034 is 2% of
z.
What i
s
 2% of 
z
?
z
2
100
x
z
 i
s
 2% of 85
z
85
2
100
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R a t i o s
A 
ratio
is a comparison of two quantities measured in the same units. Ratios are represented with a colon or as
a fraction:
x
:
y
x
y
3:2
3
2
a
:9
9
a
Examples
If a store sells apples and oranges at a ratio of 2:5, it means that for every two apples the store sells, it sells 5
oranges.
If the ratio of boys to girls in a school is 13:15, it means that for every 13 boys, there are 15 girls.
Ratio problems may ask you to determine the number of items in a group based on a ratio. You can use the
concept of multiples to solve these problems.
Example
A box contains 90 buttons, some blue and some white. The ratio of the number of blue to white buttons is 12:6.
How many of each color button is in the box?
We know there is a ratio of 12 blue buttons to every 6 white buttons. This means that for every batch of
12 buttons in the box there is also a batch of 6 buttons. We also know there is a total of 90 buttons. This means
that we must determine how many batches of blue and white buttons add up to a total of 90. So let’s write an
equation:
12
x
6
x
90, where 
x
is the number of batches of buttons
18
x
90
x
5
So we know that there are 5 batches of buttons.
Therefore, there are (5 
12) 
60 blue buttons and (5 
6) 
30 white buttons.
A 
proportion
is an equality of two ratios.
6
x
4
7
3
1
5
2
a
You can use proportions to solve ratio problems that ask you to determine how much of something is needed
based on how much you have of something else.
Example
A recipe calls for peanuts and raisins in a ratio of 3:4, respectively. If Carlos wants to make the recipe with 9
cups of peanuts, how many cups of raisins should he use? 
Let’s set up a proportion to determine how many cups of raisins Carlos needs.