286 MCGRAW-HILL’S SAT

Concept Review 4

1. distance to time


2. a sum to the number of terms in the sum


3. A proportion is a statement that two fractions or
   ratios are equal to each other.


4. If two fractions are equal, then the two “cross-
   products” must also be equal.


5. a) 6 =xy b) c)


6. $4,800, $7,200, and $12,000. The sum of the parts
   is 2 + 3 + 5 =10, so the parts are 2/10, 3/10, and
   5/10 of the whole.


7. 
   
   
   
   4. 
      
   
   
   
   

Cross-multiply: 25 x=6,000

Divide by 25: x=240 minutes

Convert to hours: 240 mins^1 hour 4

60 mins

× hrs

⎛

⎝⎜

⎞

⎠⎟=

25 bottles

6 minutes

=

1,000 bottles

xminutes

2

y 3

x

(^3) =
x 2
y

8.m^2. “At this rate.. .” implies a proportion:
Cross-multiply: m^2 x=?x
Divide by x: m^2 =?

9. 12.5. Because
   1 ⏐⏐
   2 ; ∆ABCis similar to ∆ADE.
   Thus,. Substituting xfor DEgives

.

Cross-multiply: 4 x= 50

Divide by 4: x=12.5

10. 
    
    
    
    30. Since the ratios are the same,.
        Cross-multiply: bg= 324
        Substitute bfor g: b^2 = 324
        Take the square root: b= 18
        So the number of students in Class A = 12 + 18 =30.
    
    
    
    

12

g 27

b

=

4

46

5

+

=

x

AC

AE

BC

=DE

m

xmx

meteorites

days

? meteorites

days

=

Answer Key 4: Ratios and Proportions

SAT Practice 4

1.1,000. .03 ×.2 =6/x
Simplify: .006 =6/x
Multiply by x: .006x= 6
Divide by .006: x=1,000

2.D Moving three green marbles from Jar B to Jar
A leaves three green marbles and six red marbles
in Jar A and one green marble and two red marbles
in Jar B. 3:6 =1:2.

3.B 2:3 is a “part to part” ratio, with a sum of 5.
Therefore 2/5 of the students are girls and 3/5 are
boys. 2/5 of 90 =36.

4.D Cross-multiply: 5(x) =3(y+1)
Simplify: 5 x= 3 y+ 3
Add 1: 5 x+ 1 = 3 y+ 4

5.D Since the map is “to scale,” the correspond-
ing measures are proportional:

Cross-multiply: ?x=4(x+2)

Divide by x:

6.D The ratio is a “ratio of parts” with a sum of
1 + 2 + 3 + 4 =10. The largest part, then, is 4/10 of
the whole. 4/10 of 3,600 =.4 ×3,600 =1,440.

?=

42 ()x+

x

xx

4

2

=

+

?

7.100. “At this rate” implies a proportion:

Cross-multiply:

Multiply by :

8.B

Set up the proportion:

Cross-multiply: 7.5x= 105

Divide by 7.5: x=14 feet

Find the area: Area = 21 × 14 =294 ft^2

9.C Each ratio is a “ratio of parts.” In the purple

dye, the red dye is 3/(3 +4), or 3/7, of the total, and

in the orange dye, the red dye is 3/(3 +2), or 3/5, of

the total. If the mixture is half purple and half

orange, the fraction of red is

1

2

3

7

1

2

3

5

3

14

3

10

72

140

18

35

⎛

⎝⎜

⎞

⎠⎟+

⎛

⎝⎜

⎞

⎠⎟=+= =

75

5

. 21

=

x

7.5 cm

5 cm

21 feet

x feet

x=× = =

5

2

40

200

2

100 miles

5

2

2

5

x= 40

2

5 5

gallon

8miles

gallons

miles

=

x