1001 Algebra Problems.PDF

186. b.
     4– 3 ^2 x– 1 = ^12 – y
     6 4– 3 ^2 x– 61 = 6^12 – y
     2(4 – 2x) – 6 = 3(1 – y)
     8 – 4x– 6 = 3 – 3y
     2 – 4x= 3 – 3y
     3 y= 1 + 4x
     y=


187. e.Let xbe the smallest of five consecutive odd
     integers. The next four consecutive odd integers
     are given by x+2,x+ 4,x+ 6, and x+ 8. The
     average of these five integers is equal to their
     sum divided by 5, which is expressed symboli-
     cally by. Since
     this quantity is given as –21, we must solve the
     equation = –21,
     as follows:

= –21

= –21

x+ 4 = –21

x= –25

Thus, the least of the five integers is –25.

188. a.First, we solve ab+ 6 = 4 for a:
     ab+ 6 = 4
     ab= –2
     a= –2b

Next, substitute this expression for ainto the

equation –6b+ 2a– 25 = 5 and solve for b:

–6b+ 2a– 25 = 5

–6b+ 2(–2b) – 25 = 5

–6b–4b– 25 = 5

–10b– 25 = 5

–10b= 30

b= –3

Plugging this in for bin the expression a= –2b

yields a= –2(–3) = 6. Finally, we substitute

these numerical values for aand binto ab

2

to

obtain – 63 

2

= –^12 

2

= ^14 .

189. d.Let x be the unknown number. The sentence
     “Three more than one-fourth of a number is
     three less than the number” can be expressed
     as the equation ^14 x+ 3 = x– 3. We must solve
     this equation for xas follows:

^14 x+ 3 = x– 3

4 (^14 x+ 3) = 4(x– 3)

x+ 12 = 4x– 12

x+ 24 = 4x

24 = 3x

x= 8

190. c.
     (2 – x)^52 x––x^2 = (2 – x)y
     5 x– 2 = y(2 – x)
     5 x– 2 = 2y– xy
     5 x+xy= 2 + 2y
     x(5 + y)= 2 + 2y
     x=


191. b.Solve this problem by determining the
     weight of each portion. The sum of the
     weights of the initial corn is equal to the
     weight of the final mixture. Therefore,

(20 bushels)+

(xbushels)=

[(20 + x) bushels]

Suppressing units yields the equation 20 56

+ 50x = (x+ 20)54.

54 pounds

bushel

50 pounds

bushel

56 pounds

bushel

2 + 2y

5 + y

^5 x+ 20

5

x+ (x+ 2) + (x+ 4) + (x+ 6) + (x+ 8)

5

x+ (x+ 2) + (x+ 4) + (x+ 6) + (x+ 8)

5

x+ (x+ 2) + (x+ 4) + (x+ 6) + (x+ 8)

5

1 + 4x

3

ANSWERS & EXPLANATIONS–