Sat math Essentials

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P R O B L E M S O LV I N G
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1 5 6

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3
4
9
r
This proportion means that 3 parts peanuts to 4 parts raisins must equal 9 parts peanuts to 
r
parts raisins. We
can solve for 
r
by finding cross products:
3
4
9
r
3
r
4 
9
3
r
36
3
3
r
3
3
6
r
12
Therefore, if Carlos uses 9 cups of peanuts, he needs to use 12 cups of raisins.
Practice Question 
A painter mixes red, green, and yellow paint in the ratio of 6:4:2 to produce a new color. In order to make 6
gallons of this new color, how many gallons of red paint must the painter use?
a.
1
b.
2
c.
3
d.
4
e.
6
Answer
c.
In the ratio 6:4:2, we know there are 6 parts red paint, 4 parts green paint, and 2 parts yellow paint.
Now we must first determine how many total parts there are in the ratio:
6 parts red 
4 parts green 
2 parts yellow 
12 total parts
This means that for every 12 parts of paint, 6 parts are red, 4 parts are green, and 2 parts are yellow. We
can now set up a new ratio for red paint:
6 parts red paint:12 total parts 
6:12 
1
6
2
Because we need to find how many gallons of red paint are needed to make 6 total gallons of the new
color, we can set up an equation to determine how many parts of red paint are needed to make 6 total
parts:
r
p
6
a
p
rt
a
s
r
r
t
e
s
d
to
p
t
a
a
i
l
nt
6
1
p
2
ar
p
ts
ar
r
t
e
s
d
to
p
t
a
a
i
l
nt
6
r
1
6
2
Now let’s solve for 
r
:
6
r
1
6
2
Find cross products.
12
r
6 
6
1
1
2
2
r
3
1
6
2
r
3
Therefore, we know that 3 parts red paint are needed to make 6 total parts of the new color. So 3 gal-
lons of red paint are needed to make 6 gallons of the new color.