August Answer:

Problem: The students at Proficient Junior High School visited the theme park for the annual end-of-summer celebration. Each student was allowed to purchase one of the following souvenirs: a t-shirt, a stuffed animal, or a hat. The school was given special rates: the t-shirts cost $7.00 each; the stuffed animals cost $5.00 each, and the hats cost $6.00 each. From the school, 65 students bought a souvenir, and the total bill (tax exempt, of course) was $398.00. How many of each souvenir was purchased at the amusement park?

Solution:

There are several ways to answer this question. Here's the first answer:

1) Since three pieces of data need to be organized, a chart or list is very useful. Creating a chart with three columns allows the data to be viewed at the same time.

2) The criteria are: three types of souvenirs are purchased; a total of $398.00 is spent; and, 65 sourvenirs are purchased.

3) Combinations totaling 65 souvenirs must be examined to find which will total $398.00.

T-Shirts - $7.00

Animals – $5.00

Hats - $6.00

Number

$7

$5

$6

1

$14

$10

$12

2

$21

$15

$18

3

$28

$20

$24

4

$35

$25

$30

5

$42

$30

$36

6

$49

$35

$42

7

$56

$40

$48

8

$63

$45

$54

9

$70

$50

$60

10

$77

$55

$66

11

$84

$60

$72

12

$91

$65

$78

13

$98

$70

$84

14

$105

$75

$90

15

$112

$80

$96

16

$119

$85

$102

17

$126

** $90 **

$108

18

$133

$95

$114

19

$140

$100

$120

20

$147

$105

** $126 **

21

$154

$110

$132

22

$161

$115

$138

23

$168

$120

$144

24

$175

$125

$150

25

** $182 **

$130

$156

26

$189

$135

$162

27

$196

$140

$168

28

$203

$145

$174

29

$210

$150

$180

30


Another way to answer the question is to use equations:

x=number of $7 t-shirts
 y=number of $5 animals z=number of $6 hats

x+y+z=65

7x+5y+6z=398

-7x-7y-7z=-455

7x+5y+6z=398
________________

-2y-z=-57

2y+z=57

z=57-2y

substitute 57-2y for z

x+y+57-2y=65

x-y=8

x+y+8

Now, try some different y values.

$7+$5+$6=$18 398/18=22+, so try 20ish values...

try y=20

x=y+8

x=28

z=57-2y

z=17

so to check...

28x7=196

20x5=100

17x6=102

these must add up to $398............196+100+102=398 It works!

The solution I gave would look like this...

y=18

x=y+8

x=26

z=57-2y

z=21

so to check...

26x7=182

18x5=90

21x6=126

these must add up to $398......182+90+126=398

There are probably many more variables, by plugging in for y and going from there.

This problem gave 3 variables abd 2 equations (or conditions). Consequently, it has more than one solution.

Others to check:

t-shirts animals hats
10 2 53
11 3 51
12 4 49
13 5 47
14 6 45
15 7 43
16 8 41
17 9 39

and on we go!!!

No students submitted the correct answer this month. We hope you'll try again soon!