286 MCGRAW-HILL’S SAT
Concept Review 4
- distance to time
- a sum to the number of terms in the sum
- A proportion is a statement that two fractions or
ratios are equal to each other. - If two fractions are equal, then the two “cross-
products” must also be equal. - a) 6 =xy b) c)
- $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.
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 =?
- 12.5. Because 1 ⏐⏐ 2 ; ∆ABCis similar to ∆ADE.
Thus,. Substituting xfor DEgives
.
Cross-multiply: 4 x= 50
Divide by 4: x=12.5
- 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.
- Since the ratios are the same,.
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