1
00:00:00,000 --> 00:00:00,750


2
00:00:00,750 --> 00:00:01,580
J.T.

3
00:00:01,580 --> 00:00:05,320
subscribes to a cell phone texting plan with three other

4
00:00:05,320 --> 00:00:06,759
members of his family.

5
00:00:06,759 --> 00:00:11,160
Within any given month, they cannot send more than 500 text

6
00:00:11,160 --> 00:00:12,040
messages total.

7
00:00:12,039 --> 00:00:17,329
So they cannot send more than 500 text messages total.

8
00:00:17,329 --> 00:00:19,369
At the end of this month, J.T.

9
00:00:19,370 --> 00:00:22,500
had sent 25 more texts than his older sister.

10
00:00:22,500 --> 00:00:23,309
Let me highlight.

11
00:00:23,309 --> 00:00:25,140
Let me do this in different colors.

12
00:00:25,140 --> 00:00:27,539
So at the end of the month, J.T.

13
00:00:27,539 --> 00:00:32,869
had sent 25 more texts than his older sister, 50 fewer

14
00:00:32,869 --> 00:00:41,859
texts than his younger sister, and 125 more

15
00:00:41,859 --> 00:00:44,009
texts than his mother.

16
00:00:44,009 --> 00:00:46,429
How may texts could J.T.

17
00:00:46,429 --> 00:00:55,129
have sent if they did not go over the 500-text limit?

18
00:00:55,130 --> 00:01:00,030
So let's just define some variables over here.

19
00:01:00,030 --> 00:01:01,789
Well, let's say o.s.

20
00:01:01,789 --> 00:01:07,120
o dot s is, well let's just say o, o is for older sister.

21
00:01:07,120 --> 00:01:13,383
So this is number of texts by older sister.

22
00:01:13,382 --> 00:01:17,879


23
00:01:17,879 --> 00:01:23,420
Let's say that y is equal to number of texts

24
00:01:23,420 --> 00:01:24,670
by his younger sister.

25
00:01:24,670 --> 00:01:30,170


26
00:01:30,170 --> 00:01:37,150
And then we'll use m is equal to the number of

27
00:01:37,150 --> 00:01:39,910
texts by his mother.

28
00:01:39,909 --> 00:01:42,739


29
00:01:42,739 --> 00:01:45,539
And we'll use j for a number of texts by J.T.

30
00:01:45,540 --> 00:01:51,790


31
00:01:51,790 --> 00:01:55,400
So the total number of texts that everyone sent cannot be

32
00:01:55,400 --> 00:01:56,910
more than 500.

33
00:01:56,909 --> 00:02:01,140
So if we take the sum of J.T.'s texts, plus his older

34
00:02:01,140 --> 00:02:06,359
sister's texts, plus his younger sister's texts, plus

35
00:02:06,359 --> 00:02:12,580
his mother's texts, they all have to be less than or equal

36
00:02:12,580 --> 00:02:15,410
to 500 total texts.

37
00:02:15,409 --> 00:02:18,419
Right, it can't be more than 500, so the sum has to be less

38
00:02:18,419 --> 00:02:21,229
than or equal to 500.

39
00:02:21,229 --> 00:02:24,289
Now, how can we express each of these in terms of the

40
00:02:24,289 --> 00:02:25,409
number of texts J.T.

41
00:02:25,409 --> 00:02:25,789
sent?

42
00:02:25,789 --> 00:02:28,060
Well, they give us some information here.

43
00:02:28,060 --> 00:02:29,560
This first statement, J.T.

44
00:02:29,560 --> 00:02:32,909
had sent 24 more texts than his older sister.

45
00:02:32,909 --> 00:02:39,569
So j is equal to 25 plus the number of texts of his older

46
00:02:39,569 --> 00:02:41,549
sister, which we say is o.

47
00:02:41,550 --> 00:02:44,640
It's not a 0, that's an o for older sister.

48
00:02:44,639 --> 00:02:46,250
And they also tell us that J.T.

49
00:02:46,250 --> 00:02:52,509
sent 50 fewer texts than his younger sister, so j is also

50
00:02:52,509 --> 00:02:57,129
equal to the younger sister minus 50, right?

51
00:02:57,129 --> 00:02:59,599
50 fewer texts than his younger sister.

52
00:02:59,599 --> 00:03:03,879
And then finally, they say 125 more texts than his mother, so

53
00:03:03,879 --> 00:03:09,409
j is equal to mother plus 125.

54
00:03:09,409 --> 00:03:12,250
Now, I want this equation all in terms of j's, because we

55
00:03:12,250 --> 00:03:14,430
want to say how many texts could J.T.

56
00:03:14,430 --> 00:03:15,140
have sent.

57
00:03:15,139 --> 00:03:17,989
So I want all of these expressed in j, so let's just

58
00:03:17,990 --> 00:03:22,600
solve each of these for o in terms of j, solve for y in

59
00:03:22,599 --> 00:03:25,109
terms of j, solve for m in terms of j, and then we can

60
00:03:25,110 --> 00:03:27,910
substitute back over here.

61
00:03:27,909 --> 00:03:32,639
So if j is equal to 25 plus o, if we subtract 25 from both

62
00:03:32,639 --> 00:03:38,919
sides of this equation, we get j minus 25 is equal to o.

63
00:03:38,919 --> 00:03:40,459
These are the same thing.

64
00:03:40,460 --> 00:03:43,090
If you just take this and subtract 25 from both sides,

65
00:03:43,090 --> 00:03:45,490
you get that right there.

66
00:03:45,490 --> 00:03:49,159
Now here, if you add 50 to both sides of this equation,

67
00:03:49,159 --> 00:03:54,000
if you add to 50 to both sides of this equation, j plus 50 is

68
00:03:54,000 --> 00:03:56,840
equal to the number of texts that his younger sister sent.

69
00:03:56,840 --> 00:03:59,520
I just added 50 to both sides.

70
00:03:59,520 --> 00:04:02,490
And then over here, if you subtract 125 from both sides

71
00:04:02,490 --> 00:04:06,570
of this equation-- scroll over a little bit-- if you subtract

72
00:04:06,569 --> 00:04:11,129
125 from both sides, you get j minus 125 is equal to the

73
00:04:11,129 --> 00:04:13,210
number of texts sent by his mother.

74
00:04:13,210 --> 00:04:14,370
And we could have gone straight here.

75
00:04:14,370 --> 00:04:17,829
This first statement, J.T. has sent 25 more texts than is

76
00:04:17,829 --> 00:04:18,730
older sister.

77
00:04:18,730 --> 00:04:20,290
So if you take the number of texts J.T.

78
00:04:20,290 --> 00:04:23,620
sent, subtracted 25, you'd get the number of texts by his

79
00:04:23,620 --> 00:04:24,430
older sister.

80
00:04:24,430 --> 00:04:26,319
That is an o, it is not a 0.

81
00:04:26,319 --> 00:04:27,719
o for older.

82
00:04:27,720 --> 00:04:30,600
Likewise, he sent 50 fewer texts than his younger sister,

83
00:04:30,600 --> 00:04:33,150
so if you took the number of texts he sent, add 50 to it,

84
00:04:33,149 --> 00:04:35,560
you're going to get how many his younger sister had sent.

85
00:04:35,560 --> 00:04:38,545
And then finally, he sent 125 more than his mother, so if

86
00:04:38,545 --> 00:04:42,009
you took J.T.'s texts, you take out 125, then that's how

87
00:04:42,009 --> 00:04:43,750
many his mother sent.

88
00:04:43,750 --> 00:04:47,180
So now that we have this, we can substitute for each of

89
00:04:47,180 --> 00:04:49,530
these variables into the original equation.

90
00:04:49,529 --> 00:04:53,504
So you have J.T.'s texts, plus his older sister's texts.

91
00:04:53,504 --> 00:04:56,790
But we know that o is the same thing as J.T.'s texts minus

92
00:04:56,790 --> 00:05:01,080
25, so we write J.T.'s texts minus 25.

93
00:05:01,079 --> 00:05:03,919
And then you have plus his younger sister's texts, but we

94
00:05:03,920 --> 00:05:09,650
know that's J.T.'s texts plus 50.

95
00:05:09,649 --> 00:05:12,539
And then you have his mother's texts, but his mother's texts

96
00:05:12,540 --> 00:05:18,680
are just J.T.'s texts minus 125, so plus j minus 125.

97
00:05:18,680 --> 00:05:23,560
And all of that has to be less than or equal to 500.

98
00:05:23,560 --> 00:05:24,589
So let's add the j's.

99
00:05:24,589 --> 00:05:29,289
We have 1, 2, 3, 4 j's, so you have 4 j's.

100
00:05:29,290 --> 00:05:30,879
And let's add the constants.

101
00:05:30,879 --> 00:05:38,519
You have a negative 25 plus a 50, which is 25.

102
00:05:38,519 --> 00:05:44,139
And then you have 25 minus 125, so 25 minus 125 is

103
00:05:44,139 --> 00:05:45,009
negative 100.

104
00:05:45,009 --> 00:05:49,120
So 4j minus 100-- I just added all the constant terms-- has

105
00:05:49,120 --> 00:05:54,610
to be less than or equal to 500.

106
00:05:54,610 --> 00:05:57,810
And now this is a pretty straightforward inequality.

107
00:05:57,810 --> 00:06:05,030
Add 100 to both sides and we get 4j-- these cancel out-- we

108
00:06:05,029 --> 00:06:09,529
get 4j is less than or equal to 600.

109
00:06:09,529 --> 00:06:12,639
Divide both sides by 4-- don't have to worry about the

110
00:06:12,639 --> 00:06:18,079
inequality since 4 is a positive number-- and we get j

111
00:06:18,079 --> 00:06:21,849
is less than or equal to 150.

112
00:06:21,850 --> 00:06:22,720
So J.T.

113
00:06:22,720 --> 00:06:28,560
had to send less than or equal, he had to send 150 or

114
00:06:28,560 --> 00:06:32,209
fewer texts in that month in order for all the constraints

115
00:06:32,209 --> 00:06:36,279
to match up and for the family as a combined unit to send

116
00:06:36,279 --> 00:06:38,629
less than 500.

117
00:06:38,629 --> 00:06:39,332