forked from Khan/khan-exercises
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathage_word_problems.html
192 lines (164 loc) · 13.6 KB
/
age_word_problems.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
<!DOCTYPE html>
<html data-require="math math-format word-problems spin">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Age word problems</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="problems">
<div id="solve-older-1">
<div class="vars">
<var id="C">randRange(3, 5)</var>
<var id="B">randRange(2, 20)</var>
<var id="A">randRange(1, 10) * (C - 1)</var>
</div>
<div class="question">
<p class="spin">
{<var>person(1)</var> is <var>A</var> years older than <var>person(2)</var>|<var>person(2)</var> is <var>A</var> years younger than <var>person(1)</var>}.
{For the last {four|3|two} years, <var>person(1)</var> and <var>person(2)</var> have been going to the same school.|<var>person(1)</var> and <var>person(2)</var> first met 3 years ago.|}
<var>Cardinal(B)</var> years ago, <var>person(1)</var> was <var>C</var> times {as old as|older than} <var>person(2)</var>.</p>
<p>How old is <var>person(1)</var> now?</p>
</div>
<div class="solution"><var>(C * (B + A) - B) / (C - 1)</var></div>
<div class="hints">
<p>Let <var>person(1)</var>'s current age be <code><var>personVar(1)</var></code>.</p>
<p>That means that <var>B</var> years ago, <var>person(1)</var> was <code><var>personVar(1)</var> - <var>B</var></code> years old.</p>
<p><var>person(2)</var> is <code><var>personVar(1)</var> - <var>A</var></code> years old right now, so <var>B</var> years ago, <var>he(2)</var> was <code>(<var>personVar(1)</var> - <var>A</var>) - <var>B</var> = <var>personVar(1)</var> - <var>A + B</var></code> years old.</p>
<p><var>person(1)</var> was <var>C</var> times as old as <var>person(2)</var>, so that means <code><var>personVar(1)</var> - <var>B</var> = <var>C</var> (<var>personVar(1)</var> - <var>A + B</var>)</code>.</p>
<p>Expand: <code><var>personVar(1)</var> - <var>B</var> = <var>C</var> <var>personVar(1)</var> - <var>C * (A + B)</var></code>.</p>
<p>Solve for <code><var>personVar(1)</var></code> to get <code><var>C - 1</var> <var>personVar(1)</var> = <var>C * (A + B) - B</var></code>; <code><var>personVar(1)</var> = <var>(C * (B + A) - B) / (C - 1)</var></code>.</p>
</div>
</div>
<div id="solve-younger-1" data-type="solve-older-1">
<div class="question">
<p><var>person(1)</var> is <var>A</var> years older than
<var>person(2)</var>. <var>Cardinal(B)</var> years ago, <var>person(1)</var>
was <var>C</var> times as old as <var>person(2)</var>.</p>
<p>How old is <var>person(2)</var> now?</p>
</div>
<div class="solution"><var>(A - B + C * B) / (C - 1)</var></div>
<div class="hints">
<p>Let <var>person(2)</var>'s current age be <code><var>personVar(2)</var></code>.</p>
<p>That means that <var>person(1)</var> is currently <code><var>personVar(2)</var> + <var>A</var></code> years old and <var>B</var> years ago, <var>person(1)</var> was <code>(<var>personVar(2)</var> + <var>A</var>) - <var>B</var> = <var>personVar(2)</var> + <var>A - B</var></code> years old.</p>
<p><var>Cardinal(B)</var> years ago, <var>person(2)</var> was <code><var>personVar(2)</var> - <var>B</var></code> years old.</p>
<p><var>person(1)</var> was <var>C</var> times as old as <var>person(2)</var>, so that means <code><var>personVar(2)</var> + <var>A - B</var> = <var>C</var> (<var>personVar(2)</var> - <var>B</var>)</code>.</p>
<p>Expand: <code><var>personVar(2)</var> + <var>A - B</var> = <var>C</var> <var>personVar(2)</var> - <var>C * B</var></code>.</p>
<p>Solve for <code><var>personVar(2)</var></code> to get <code><var>C - 1</var> <var>personVar(2)</var> = <var>A - B + C * B</var></code>; <code><var>personVar(2)</var> = <var>(A - B + C * B) / (C - 1)</var></code>.</p>
</div>
</div>
<div id="solve-older-2">
<div class="vars">
<var id="C">randRange(3, 5)</var>
<var id="A">randRange(2, 10) * (C - 1)</var>
</div>
<div class="question">
<p><var>person(1)</var> is <var>C</var> times as old as
<var>person(2)</var> and is also <var>A</var>
years older than <var>person(2)</var>.</p>
<p>How old is <var>person(1)</var>?</p>
</div>
<div class="solution"><var>A * C / (C - 1)</var></div>
<div class="hints">
<p>Let <var>person(1)</var>'s age be <code><var>personVar(1)</var></code>.</p>
<p>We know <var>person(2)</var> is <code>1/<var>C</var></code> as old as <var>person(1)</var>, so <var>person(2)</var>'s age can be written as <code><var>personVar(1)</var> / <var>C</var></code>.</p>
<p><var>His(2)</var> age can also be written as <code><var>personVar(1)</var> - <var>A</var></code>.</p>
<p>Set the two expressions for <var>person(2)</var>'s age equal to each other: <code><var>personVar(1)</var> / <var>C</var> = <var>personVar(1)</var> - <var>A</var></code>.</p>
<p>Multiply both sides by <code><var>C</var></code> to get <code><var>personVar(1)</var> = <var>C</var> <var>personVar(1)</var> - <var>A * C</var></code>.</p>
<p>Solve for <code><var>personVar(1)</var></code> to get <code><var>C - 1</var> <var>personVar(1)</var> = <var>A * C</var></code>; <code><var>personVar(1)</var> = <var>A * C / (C - 1)</var></code>.</p>
</div>
</div>
<div id="solve-younger-2" data-type="solve-older-2">
<div class="question">
<p><var>person(1)</var> is <var>C</var> times as old as
<var>person(2)</var> and is also <var>A</var>
years older than <var>person(2)</var>.</p>
<p>How old is <var>person(2)</var>?</p>
</div>
<div class="solution"><var>A / (C - 1)</var></div>
<div class="hints">
<p>Let <var>person(2)</var>'s age be <code><var>personVar(2)</var></code>.</p>
<p>We know <var>person(1)</var> is <var>C</var> times as old as <var>person(2)</var>, so <var>person(1)</var>'s age can be written as <code><var>C</var> <var>personVar(2)</var></code>.</p>
<p><var>His(1)</var> age can also be written as <code><var>personVar(2)</var> + <var>A</var></code>.</p>
<p>Set the two expressions for <var>person(1)</var>'s age equal to each other: <code><var>C</var> <var>personVar(2)</var> = <var>personVar(2)</var> + <var>A</var></code>.</p>
<p>Solve for <code><var>personVar(2)</var></code> to get <code><var>C - 1</var> <var>personVar(2)</var> = <var>A</var></code>; <code><var>personVar(2)</var> = <var>A / (C - 1)</var></code>.</p>
</div>
</div>
<div id="solve-older-3">
<div class="vars" data-ensure="C - A !== A && A * B * (C - 1) < 100 * (C - A)">
<var id="A">randRange(2, 5)</var>
<var id="C">randRange(A + 2, 9)</var>
<var id="B">randRange(2, 7) * (C - A)</var>
</div>
<div class="question">
<p><var>person(1)</var> is <var>A</var> times as old as <var>person(2)</var>. <var>Cardinal(B)</var> years ago, <var>person(1)</var> was <var>C</var> times as old as <var>person(2)</var>.</p>
<p>How old is <var>person(1)</var> now?</p>
</div>
<div class="solution"><var>A * B * (C - 1) / (C - A)</var></div>
<div class="hints">
<p>Let <var>person(1)</var>'s age be <code><var>personVar(1)</var></code>.</p>
<p>We know <var>person(2)</var> is <code>1/<var>A</var></code> as old as <var>person(1)</var>, so <var>person(2)</var>'s age can be written as <code><var>personVar(1)</var> / <var>A</var></code>.</p>
<p><var>B</var> years ago, <var>person(1)</var> was <code><var>personVar(1)</var> - <var>B</var></code> years old and <var>person(2)</var> was <code><var>personVar(1)</var> / <var>A</var> - <var>B</var></code> years old.</p>
<p>At that time, <var>person(1)</var> was <var>C</var> times as old as <var>person(2)</var>, so we can write <code><var>personVar(1)</var> - <var>B</var> = <var>C</var> (<var>personVar(1)</var> / <var>A</var> - <var>B</var>)</code>.</p>
<p>Expand: <code><var>personVar(1)</var> - <var>B</var> = <var>fractionReduce(C, A)</var> <var>personVar(1)</var> - <var>C * B</var></code>.</p>
<p>Solve for <code><var>personVar(1)</var></code> to get <code><var>fractionReduce(C - A, A)</var> <var>personVar(1)</var> = <var>B * (C - 1)</var></code>; <code><var>personVar(1)</var> = <var>fractionReduce(A, C - A)</var> \cdot <var>B * (C - 1)</var> = <var>A * B * (C - 1) / (C - A)</var></code>.</p>
</div>
</div>
<div id="solve-younger-3" data-type="solve-older-3">
<div class="question">
<p><var>person(1)</var> is <var>A</var> times as old as <var>person(2)</var>. <var>Cardinal(B)</var> years ago, <var>person(1)</var> was <var>C</var> times as old as <var>person(2)</var>.</p>
<p>How old is <var>person(2)</var> now?</p>
</div>
<div class="solution"><var>B * (C - 1) / (C - A)</var></div>
<div class="hints">
<p>Let <var>person(2)</var>'s age be <code><var>personVar(2)</var></code>.</p>
<p>We know <var>person(1)</var> is <var>A</var> times as old as <var>person(2)</var>, so <var>person(1)</var>'s age can be written as <code><var>A</var> <var>personVar(2)</var></code>.</p>
<p><var>Cardinal(B)</var> years ago, <var>person(1)</var> was <code><var>A</var> <var>personVar(2)</var> - <var>B</var></code> years old and <var>person(2)</var> was <code><var>personVar(2)</var> - <var>B</var></code> years old.</p>
<p>At that time, <var>person(1)</var> was <var>C</var> times as old as <var>person(2)</var>, so we can write <code><var>A</var> <var>personVar(2)</var> - <var>B</var> = <var>C</var> (<var>personVar(2)</var> - <var>B</var>)</code>.</p>
<p>Expand: <code><var>A</var> <var>personVar(2)</var> - <var>B</var> = <var>C</var> <var>personVar(2)</var> - <var>B * C</var></code>.</p>
<p>Solve for <code><var>personVar(2)</var></code> to get <code><var>C - A</var> <var>personVar(2)</var> = <var>B * (C - 1)</var></code>; <code><var>personVar(2)</var> = <var>B * (C - 1) / (C - A)</var></code>.</p>
</div>
</div>
<div id="solve-single-4" data-weight="2">
<div class="vars" data-ensure="B <= 60">
<var id="A">randRange(3, 20)</var>
<var id="B">randRange(7, 24) * (A - 1)</var>
</div>
<div class="question">
<p>In <var>B</var> years, <var>person(1)</var> will be <var>A</var> times as old as <var>he(1)</var> is right now.</p>
<p>How old is <var>he(1)</var> right now?</p>
</div>
<div class="solution"><var>B / (A - 1)</var></div>
<div class="hints">
<p>Let <var>person(1)</var>'s age be <code><var>personVar(1)</var></code>.</p>
<p>In <var>B</var> years, <var>he(1)</var> will be <code><var>personVar(1)</var> + <var>B</var></code> years old.</p>
<p>At that time, <var>he(1)</var> will also be <code><var>A</var> <var>personVar(1)</var></code> years old.</p>
<p>We write <code><var>personVar(1)</var> + <var>B</var> = <var>A</var> <var>personVar(1)</var></code>.</p>
<p>Solve for <code><var>personVar(1)</var></code> to get <code><var>A - 1</var> <var>personVar(1)</var> = <var>B</var></code>; <code><var>personVar(1)</var> = <var>B / (A - 1)</var></code>.</p>
</div>
</div>
<div id="solve-single-5" data-weight="2">
<div class="vars" data-ensure="A <= 80 && B >= 2 && (A - B * C) > (C - 1)">
<var id="C">randRange(3, 5)</var>
<var id="B">randRange(1, 10) * (C - 1)</var>
<var id="A">randRange(C * B + 1, 15) * (C - 1)</var>
</div>
<div class="question">
<p><var>person(1)</var> is <var>A</var> years old and <var>person(2)</var> is <var>B</var> years old.</p>
<p>How many years will it take until <var>person(1)</var> is only <var>C</var> times as old as <var>person(2)</var>?</p>
</div>
<div class="solution"><var>(A - B * C) / (C - 1)</var></div>
<div class="hints">
<p>Let <code>y</code> be the number of years that it will take.</p>
<p>In <code>y</code> years, <var>person(1)</var> will be <code><var>A</var> + y</code> years old and <var>person(2)</var> will be <code><var>B</var> + y</code> years old.</p>
<p>At that time, <var>person(1)</var> will be <var>C</var> times as old as <var>person(2)</var>.</p>
<p>We write <code><var>A</var> + y = <var>C</var> (<var>B</var> + y)</code>.</p>
<p>Expand to get <code><var>A</var> + y = <var>C * B</var> + <var>C</var> y</code>.</p>
<p>Solve for <code>y</code> to get <code><var>C - 1</var> y = <var>A - C * B</var></code>; <code>y = <var>(A - C * B) / (C - 1)</var></code>.</p>
</div>
</div>
</div>
</div>
</body>
</html>