## anonymous 5 years ago Three-fourths of seven less than a number is forty-two. Find the number.

1. anonymous

my ans is -147/4

2. anonymous

(3/4)(x-7) = 42. Gogogo

3. anonymous

$\frac{3(x-7)}{4} = 42 \rightarrow \frac{4(42)}{3} = x-7 \rightarrow x=?$

4. anonymous

so the number is 49?

5. anonymous

Close.. $x-7 = 56 \rightarrow x-7+7 = 56 +7 = x = ?$

6. anonymous

63?

7. anonymous

Indeed.

8. anonymous

ok i got another for you...i like your help

9. anonymous

The real trick here is in setting up the problem initially. Being able to convert word problems into workable equations is a good talent to develop.

10. anonymous

suzette did twice as many pushups as mark did. bonnie did five less pushups than mark did. if they did 71 pushups together how many did each do?

11. anonymous

$\text{Polpak I prefer } \implies\ \text{instead of} \rightarrow$ The latter looks to much like a limit.

12. anonymous

Let S be the number of pushups Suzette did, and M be the number Mark did, and B is the number Bonnie did. Translate this sentence into an equation. "They did 71 pushups altogether."

13. anonymous

Newton: $\lim_{n \rightarrow 0}$ Looks like a limit $\rightarrow$ doesn't. Not to me anyway. And in my homework I always use a single arrow instead of the double thing, so it feels more natural to me.

14. anonymous

$2s +m=5-m=71 ?$

15. anonymous

That's a bit of a leap. Try just using the variables I defined. If they all did 71 pushups then: $M + S + B = 71$

16. anonymous

Then we look at how M, S, and B are otherwise related.

17. anonymous

"Bonnie did 5 less pushups then Mark" $\rightarrow B = M-5$

18. anonymous

"Suzzette did twice as many pushups as mark" $\rightarrow ?$

19. anonymous

2(m)=s

20. anonymous

Right. Now, using what we know about S and B, we can go back to our original equation and find how many mark did. $M+S+B=71$ Using the fact that S=2M $\rightarrow M + 2M + B = 71$ Using the fact that B=M-5 $\rightarrow ?$

21. anonymous

im lost

22. anonymous

I plugged in 2M for S in the M + S + B = 71 equation. Now do the same for B.

23. anonymous

m-5=b

24. anonymous

Yes, that's the equation for what B _is_. Now use that in the equation M + S + B = 71

25. anonymous

im so confused

26. anonymous

B = M - 5. Would you agree then that M + S + B = M + S + (M-5) ?

27. anonymous

ok

28. anonymous

And since S = 2M Would you agree that M + S + (M-5) = M + 2M + M - 5 ?

29. anonymous

i think

30. anonymous

$S = 2M$ $\rightarrow M + S = M + 2M$ $B = M-5$ $\rightarrow M + S + B = M + S + (M-5)$ $= (M + S) + (M-5) = M + 2M + M-5$

31. anonymous

Does that make sense?

32. anonymous

not at all

33. anonymous

S = 2M S + 5 = 2M + 5 right?

34. anonymous

If S = 2M then S + SOMETHING = 2M + SOMETHING

35. anonymous

That is what equals means

36. anonymous

I don't understand what you're not understanding. Which part is confusing?

37. anonymous

im a retard when it comes to math...i dnt even know where to begin to solve ur problem

38. anonymous

Do you understand what S = 2M means? It means that anywhere you have an S, you can replace it with a 2M and it will mean the same thing.

39. anonymous

ok i understand that

40. anonymous

So if we have an equation M + S + B = 71, we can replace the S with 2M right?

41. anonymous

yea

42. anonymous

So rewrite the equation by replacing the S. Also replace the B since we know that B = M-5.

43. anonymous

M+2(M)=71?

44. anonymous

Not quite. M + 2M = 71 is the same as saying M + S is 71. But we know that's not true because M + S + B is 71 and B is not 0. M + 2M + B = 71 is true. But since we know B = M-5 we can replace B in this equation and we get?

45. anonymous

M+2M+M-5

46. anonymous

Right. Now, since we said that M + S + B = 71 and we said that M + S + B = M + 2M + M - 5 Then we know that M + 2M + M - 5 = 71 So solve for M.

47. anonymous

32m 16s 23b

48. anonymous

?

49. anonymous

thats not right

50. anonymous

$M + 2M + M -5 = 71$ $\rightarrow 4M -5 = 71$ $\rightarrow 4M = 76$ $\rightarrow M = 76/4$ $\rightarrow M = 19$

51. anonymous

38 19 14

52. anonymous

S = 2M = 2(19) = 38 B = M-5 = 19-5 = 14

53. anonymous

the sum of three numbers is -48. the first number is 12 more than the secong number, andthe third number is 20 less than twice the second number. find the three numbers.

54. anonymous

Ok. This one you're gonna need to put more of the effort into. First pick variables for each of your 3 numbers (A, B, C?). Then take each sentance and see what it's telling you about your numbers. (Try to write the sentance as an equation)

55. anonymous

The first sentance is: The sum of the three numbers is -48. So your equation is ?

56. anonymous

a+b+c=-48

57. anonymous

Perfect. Now the next sentence. The first number is 12 more than the second. Therefore?

58. anonymous

A=12+B

59. anonymous

And finally, The third number is 20 less than twice the second number.

60. anonymous

C=20-2(b)

61. anonymous

Not quite.

62. anonymous

2B = twice the second number. twenty less than twice the second number = twenty less than 2B = 2B - 20 If 2B is 10, than 20 - 10 is not twenty less than 10.

63. anonymous

20-2(b)=C

64. anonymous

No.

65. anonymous

C = 2B - 20

66. anonymous

ok

67. anonymous

?

68. anonymous

So now put them all together. You have 1 equation with all 3 elements, and 2 other equations that give you replacement values for A and C. So replace them in and solve for B.

69. anonymous

once again im lost

70. anonymous

A + B + C = -48 A = 12 + B So.. ? + B + C = -48 Fill in the ?

71. anonymous

36

72. anonymous

... No A = 12 + B. So (A) + B + C = (12+B) + B + C right??

73. anonymous

ya

74. anonymous

If A + B + C = -48 and A = 12 + B and C = 2B - 20 the (A) + B + (C) = ?

75. anonymous

Just replace the A and the C.

76. anonymous

with what?

77. anonymous

With what they equal.

78. anonymous

i cant tell you what a equals without knowing b

79. anonymous

............... You do know what A equals. A equals 12 + B. Period. It may also be represented in a different way, but you at least know that much.

80. anonymous

So put 12 + B where there is an A. And put 2B-20 where there is a C.

81. anonymous

12+b+2b-20

82. anonymous

Right. And what does that equal again?

83. anonymous

=-48

84. anonymous

So what does B equal ?

85. anonymous

Actually that's not quite right.

86. anonymous

-8

87. anonymous

you have 12 + B + 2B - 20 which equals (12+B) + (2B-20) which equals A + C. You forgot the B in the middle.

88. anonymous

Rewrite the equation again. A + B + C = -48, A = B + 12, C = 2B-20 So...

89. anonymous

idk man

90. anonymous

im dying here

91. anonymous

A + B + C = (12+B) + B + (2B-20) ^A + ^B + ^C Right?

92. anonymous

yea

93. anonymous

So if A + B + C = -48, what is B.

94. anonymous

-36

95. anonymous

$12 + B + B + 2B - 20 = -48$ $\rightarrow 4B - 20 + 12 -12 + 20 = -48 - 12 + 20$ $\rightarrow 4B = -60 + 20$ $\rightarrow 4B = -40$ $\rightarrow B = -10$ $\rightarrow A = 12 + B = 12 + -10 = 2$ $\rightarrow C = 2B-20 = -20 -20 = -40$