7th Grade Math

R10 Selected Answers and Solutions

Selected Answers and Solutions

side of the equation by _^15 instead of dividing each

side by 5. 31. Sample answer: Three coins of the

same value are worth 75 cents. How much is each

coin worth? 33. C 35a. 16.50x = 99

35b. 6 months; Sample answer: To fi nd x, divide

both sides by 16.50.

Pages 224–226 Lesson 4-2D

1.^58 3. 295 5. 2 7. -8.2 9. 54 11. 43 n = 24;
32 pieces of fruit 13. 56 or 1 51 15. 16 or 6 17. ^13
19. 418 21. 5 23. - 6 25. - 3 27. 56 or 1 ^15
2929 ^78 k = _^56

(^) ( 78 ) ^78 k = ( ^87 ) ^56
k = _^2021

31. 6 32 33. 0.5t = 3; 6 months 35. 140 = 157 x; 300 ft
    3737 If one serving is^ ^34 cup, you can fi nd how many
    servings are in 16 ^12 cups by writing an equation
    where x is the number of servings.
    43 x = 16 ^12
    43 x = ^332

(^) ( 34 ) ^34 x = ( ^43 ) ^332
x = 22
There are 22 servings in 16 _^12 cups.

39. 1.75m = 3.5; 2 movies 41. 53 , 5; The other pairs
    of numbers are reciprocals. 43. Sample answer: If
    you multiply each side of an equation by the same
    nonzero number, two sides remain equal; 52 x = 7.


40. I 47. 16 hours 49. 5 51. 450 53. - 8 55. 4


41. 
    
    
    
    • 65
    
    
    
    

Pages 232–234 Lesson 4-3B

1. 2
   33 -^6 r +^1 = -^17

• __ 1 = - 1


• 6 r = - 18
  --^66 r = --^186
  r = 3

5. 3 7. 14 c + 23 = 65; 3 CDs 9. 3 11. - 4 13. 4


6. 9 17. 8 19. 24 21. 2 c + 10 = 14; 2 cups


7. 2.25 25. 2.1 27. 11
   2929 a. F = 1.8C +^32 Write the equation.
   16 = 1.8C + 32 Substitute 16 for F.
   16 - 32 = 1.8C + 32 - 32 Subtract 32.
   _-1.8^16 = _1.81.8C Divide each side by 1.8.
   -8.9 = C Simplify.
   -9°C Round to the nearest degree.
   b. F = 1.8C + 32 Write the equation.
   F = 1.8(-11) + 32 Substitute -11 for C.

F = -19.8 + 32 Add -19.8 and 32.

F = 12.2 Simplify.

Subtract Alaska’s record low temperature from

Hawaii’s record low temperature.

12.2 - (-80) = 92.2°F

31. 22 subscriptions 33. D 35. 1 _^12 37. 20


32. 3.25n = 22.75; 7 E-cards 41. - 29 43. - 24
    Pages 238–239 Lesson 4-3D


33. Sample answer: 2x + 8 = 40; subtracted 2x from
    each side 3. Sample answer: 5x - 7 = 43;
    subtracted x from each side 5. 52
    77 3 - x =^4 -^3 x
    
    
    • 3 x = + 3 x
      3 + 2 x = 4
    
    
    
    
    
    
    • 3 = - 3
      2 x = 1
      ^22 x = ^12
      x = _^12
    
    
    
    


34. 6.9 11. Sample answer: 2x + 14 = 20; subtracted
    4 x from both sides 13. Sample answer: 3x = 36;
    subtracted 3x from both sides and added 3 to both
    sides 15. Sample answer: 2x = 20; subtracted 2x
    from both sides and added 15 to both sides 17. 6


35. 24 21. 4.2 23. - 10 25. _^14 27. - 6
    2929 Manny bought supplies for $48 and 3 buckets
    at a certain price, b. Jin bought 7 buckets at a
    certain price, b. Manny and Jin each spent the same
    amount of money, so set the expressions equal to
    each other. Then solve.
    3 b + 48 = 7 b
    
    
    • 3 b - 3 b
      48 = 4 b
      12 = b
      The cost of one bucket is $12.
    
    
    
    


36. Adding 2b to both sides and then subtracting
    14 from both sides of the fi rst equation will result
    in the second equation. 33. - 10 35. B
    37a. 15 c = 12 c + 0.99 37b. 0.33; A baseball card
    costs 33 cents. 37c. Sergio could have bought
    9 baseball cards if he bought 2 packs of gum.


37. 
    
    
    
    • 3 41. - _^35 43. 8 guests
    
    
    
    

Pages 246–248 Lesson 4-4B

1. c < 4 3. y < 20
   55 c +^4 ≥^17 Write the inequality.
   
   
   • 4 - 4 Subtract 4 from each side.
     c ≥ 13 Simplify.
   
   
   
   


2. h ≥ 6

0 1 2 3 4 5 6 7 8 9 10 11

9. 
   
   
   
   • 16 ≤ n
   
   
   • 25 - 24 - 23 - 22 - 21 - 20 - 19 - 18 - 17 - 16 - 15
   
   
   
   


10. 5 < n 13. y ≥ - 7 15. x > - 1

R01_R42_EM_SelAns_895130.indd R10 1/18/10 9:51 AM