Solving Problems Using a Table of Values: P. 137 #s 10-12
10. Heather wants to make 250 origami peace cranes for a school display. She makes 12 cranes
the first day, 15 cranes the second day, 18 cranes the third day, and so on. If she continues this
pattern for 10 days, will she reach her goal of 250 peace cranes.
Given: She wants to make 250 cranes. 1st day = 12; 2nd day = 15; 3rd day = 18
Required: If pattern continues for 10 days, will she reach her goal of 250
Make a Plan: Make a table of values with 3 columns- one to keep track of the days, the 2nd to
record the number of cranes she makes on each day, and one to record the total number of cranes
she makes, so I’ll know whether or not she reaches her goal.
Carry out the Plan:
Day
1
2
3
4
5
6
7
8
9
10
# of Cranes on Day
12
15
18
21
24
27
30
33
36
39
Total # of Cranes
12
27
45
66
90
117
147
180
216
255
Solution: Yes, she will reach her goal of 250 peace cranes, if she continues for 10 days. In 10
days, she will have made 255 cranes.
11. The school office staff has organized a telephone tree system to use in case of emergency.
The first caller phones three parents. These parents, in turn, each call three more parents, and so
on.
a) How many parents will receive a call on the third round of calls?
b) How many parents in total will receive calls by the end of the third round of calls?
c) If there are 363 parents to be called, how many rounds of calls will be needed?
Given: 1st caller phones 3 parents; each parent then calls 3 more parents, and it continues each
round
Required: # parents receiving a call in round 2; total # of parents called by end of round 3; # of
rounds needed to call 363 parents
Make a Plan: Make a table of values with 3 columns- one to keep track of the rounds, the 2nd to
record the number of parents called in each round, and one to record the total number of parents
called, so I’ll know when all 363 parents have been called.
Carry out the Plan:
Round
1
2
3
4
5
# of Parents Called in the
Round
3
9
27
81
243
Total # of Parents Called
3
12
39
120
363
Solutions:
a) On the 3rd round, 27 parents will receive a call.
b) By the end of the 3rd round, a total of 39 parents will have received calls.
c) If there are 363 parents to be called, 5 rounds of calls will be needed.
12. The students challenge the teachers to a basketball shootout, with the money from ticket sales
going to charity. The goal is to raise $175. On the first day, 16 tickets are sold. On the
following days, the number of tickets sold increases by three tickets per day.
a) How many tickets in total are sold by the end of the 5th day?
b) Each ticket costs $2. On which day of ticket sales will the students reach their goal?
Given: goal is to raise $175; 16 tickets sold on 1st day; 3 more tickets sold on each day after the
1st
Required: # of tickets sold by end of 5th day; day on which they’ll reach their goal
Make a Plan: Make a table of values with 4 columns- one column to keep track of the days, the
2nd to record the number of tickets sold on each day, the 3rd to record the total number of tickets
sold, and the 4th to record the number of money raised through ticket sales.
Carry out the Plan:
Day
1
2
3
4
5
Tickets Sold Each
Day
16
19
22
25
28
Total # of Tickets
Sold
16
35
57
82
110
Amount of $ Raised
($2/ticket)
$32
$70
$114
$164
$220
Solutions:
a) By the end of the 5th day, a total of 110 tickets are sold.
b) If each ticket costs $2, students will reach their goal of $175. By the end of the 5th day,
they will have raised $220.