CHAPTER 8 / ESSENTIAL ALGEBRA I SKILLS 331

Concept Review 7

1. m=Mike’s current age, d=Dave’s current age;
   m=2(d−5)


2. a=the population of town A, b=the population
   of town B; a=1.4b


3. n=number of marbles in the jar;
   n−(2/3)n= 5 +(1/6)n


4. b=number of blue marbles, r=number of red
   marbles; b= 4 + 2 r


5. c=cost of one candy bar, l=cost of one lollipop;
   3 c+ 2 l=2.20, and 4c+ 2 l=2.80.
   Subtract: 4 c+ 2 l=2.80
   
   
   • (3c+ 2 l=2.20)
     c =.60
     Plug in to find l: 3(.60) + 2 l=2.20
     Simplify: 1.80 + 2 l=2.20
     Subtract 1.80: 2 l=.40
     Divide by 2: l=.20
   
   
   
   

   6. n=number of seats in the stadium;
   
      (2/3)n−1,000 =(3/7)n

   
   

   Subtract (2/3)n: −1,000 =−(5/21)n
   Multiply by −(21/5): 4,200 =n

   
   

7.

Simplify:

Multiply by 4: 2 m+ 2 n=s+t

Subtract t: 2 m+ 2 n−t=s

8. b=value of blue chip, r=value of red chip, g=value
   of green chip; b= 2 +r, r= 2 +g,and 5g=m,so
   Cost of 10 blue and 5 red chips: 10 b+ 5 r
   Substitute b= 2 +r: 10(2 +r) + 5 r
   Simplify: 20 + 15 r
   Substitute r= 2 +g: 20 +15(2 +g)
   Simplify: 50 + 15 g
   Substitute g=m/5: 50 + 3 m

mn st+

=

⎛ +

⎝⎜

⎞

(^24) ⎠⎟
mn+ st

⎛ +

⎝⎜

⎞

(^2) ⎠⎟

1

22

Answer Key 7: Word Problems

SAT Practice 7

1.C You could test the choices here, or do the

algebra:

Multiply by x: 24 −x= 3 x

Add x: 24 = 4 x

Divide by 4: 6 =x

2.n=Nora’s current age, m=Mary’s current age.
Interpret first sentence: n− 3 =(1/2)m
Interpret second sentence: m=n+ 4
Subtract 4: m− 4 =n
Substitute n=m−4: m− 4 − 3 =(1/2)m
Simplify: m− 7 =(1/2)m
Subtract m: − 7 =−(1/2)m
Multiply by −2: 14 =m

3.E p/q=9/7, q/r=14/3.

Multiply:

4. 40 J=number of books Joan had originally.
   E=number of books Emily had originally. J= 2 E.
   After the exchange, Emily has E+5 and Joan has
   J−5 books, so J− 5 = 10 +(E+5).
   Simplify: J− 5 =E+ 15
   Subtract 15: J− 20 =E
   Substitute into J=2(J−20)
   first equation:
   Solve for J: J= 40
   (Reread and check)

5.C Let xbe the cost of living in 1960. In 1970, the cost
of living was 1.2x,and in 1980 it was 1.5x.Use the per-
cent change formula: (1.5x−1.2x)/1.2x=.25 =25%.

p

q

q

r

p

r

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

==

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

=

9

7

14

3

6

1

24

3

−

=

x

x

6. 8 Let w=the number of games won and l=the
   number of games lost. w/l=7/5 and w+l=48.
   Multiply by l: w=(7/5)l
   Substitute into 2nd eq.: (7/5)l+l= 48
   Simplify: (12/5)l= 48
   Multiply by 5/12: l= 20
   Plug in to find w: w+ 20 = 48
   Subtract 20: w= 28
   How many more games won than lost?
   w−l= 28 − 20 = 8


7. 16 Let c=number of cats originally, d=number
   of dogs originally. c/d=4/5. Now the number of
   cats is 2cand the number of dogs is d+12. If the
   ratio of dogs to cats is now 1 to 1, 2c=d+12.
   Cross-multiply: 5 c= 4 d
   Divide by 4: (5/4)c=d
   Substitute: 2 c=(5/4)c+ 12
   Subtract (5/4)c: (3/4)c= 12
   Multiply by 4/3: c=16 (Reread
   and check)
   8.C Number of sophomores =(1/4)(504) =126.
   If 3/7 of the sophomores are boys, 4/7 are girls:
   (4/7)(126) =72. If 1/3 of the sophomore girls take
   French, 2/3 do not: (2/3)(72) =48.
   9.E r, g,and bare the numbers of red, green, and
   blue marbles. r= 3 gand g= 5 b.Total marbles =
   r+g+b.
   Substitute r= 3 g:3g+g+b= 4 g+b
   Substitute g= 5 b:4(5b) +b= 21 b
   So the total must be a multiple of 21, and 42 =2(21).