CHAPTER 16 / PRACTICE TEST 2 693
- 25 First calculate how many grams of sucrose
there are in 200 grams of a 10% mixture.
(200 grams)(.10) =20 grams of sucrose
Since you will be adding xgrams of sucrose, the total
weight of sucrose will be 20 +xgrams, and the total
weight of the mixture will be 200 +xgrams. Since the
fraction that will be sucrose is 20%,
Cross-multiply: (20 +x)(100) =20(200 +x)
Distribute: 2,000 + 100 x=4,000 + 20 x
Subtract 2,000: 100 x=2,000 + 20 x
Subtract 20x: 80 x=2,000
Divide by 80: x= 25
(Chapter 7, Lesson 5: Percents)
(Chapter 7, Lesson 4: Ratios and Proportions)- 24 First calculate how long the race took.
distance=rate×time
16 =(8)(time)
Divide by 8: 2 hours =time=120 minutes
Next, find the new rate that is 25% faster:
new rate=(8)(1.25) =10 mph
Calculate how long the new race would take:
distance=rate×time
16 =(10)(time)
Divide by 10: 1.6 hours =time =96 minutes
So she can improve her time by (120 −96) =24 minutes.
(Chapter 9, Lesson 4: Rate Problems)
20
200
20
100
+
+
=
x
x- 5 Think simple: What’s the simplest way to turn
8 x+ 4 yinto 2x+y? Just divide by 4!
8 x+ 4 y= 20
Divide by 4: 2 x+y= 5(Chapter 8, Lesson 1: Solving Equations)
(Chapter 6, Lesson 4: Simplifying Problems)
- 12 Just substitute x=3 and y=5 into the equa-
tion and solve for m:
3 m− 15 = 21
Add 15: 3 m= 36
Divide by 3: m= 12
(Chapter 8, Lesson 1: Solving Equations)
(Chapter 11, Lesson 2: Functions) - 15 Ratios such as 4:5 can also be written as 4x:5x.
So the number of men mis 4xand the number of
women wis 5x.
Plug those values into the equation w=m+ 3
5 x= 4 x+ 3
Subtract 4x: x= 3
Plug 3 in to 5x: w= 5 x=5(3) = 15
(Chapter 7, Lesson 4: Ratios and Proportions)
14.8 or 12 y=⎟ 2 x−b⎟
Plug in (5, 2): 2 =⎟2(5) −b⎟
Simplify: 2 =⎟ 10 −b⎟
(10 −b)=2 or (10 −b) =− 2
Subtract 10: −b=−8 or −b=− 12
Multiply by −1: b=8 or b= 12
(Chapter 8, Lesson 6: Inequalities, Absolute Values,
and Plugging In)