Four 33¢ stamps and three 15¢ stamps
equals \$1.77 in postage.

Complete Solutions:
Several ways to do the problem:

Solution 1.
Using the hint on the first page, divide 177 by 33. With five 33¢ stamps, you have \$1.65 worth of postage and need 12 more cents. With four 33¢ stamps, you have \$1.32 worth of postage and need 45 more cents. Since three 15¢ stamps make 45¢, the solution is four 33¢ and three 15¢ stamps.

 Number of 33¢ stamps Number of 15¢ stamps Value 6 0 \$1.98 5 0 \$1.65 5 1 \$1.80 4 1 \$1.47 4 2 \$1.62 4 3 \$1.77

Solution 2.
Another strategy is to make a table (shown at left) listing all of the possible combinations of 33¢ and 15¢ stamps that can be used, without exceeding \$1.77. Then work your way up, adding 15¢ stamps.

Solution 3.
Make a combination chart
, (shown at right) and fill it out until you either reach or pass \$1.77 in every row and column. The first row has the values of an increasing number of 33¢ stamps and the first column the values of increasing the number of 15¢ stamps. Remaining cells are the combinations of the two.

 No. of 33¢ stamps 1 2 3 4 5 6 No. of 15¢ stamps \$.33 \$.66 \$.99 \$1.32 \$1.65 \$1.98 1 \$.15 \$.48 \$.81 \$1.14 \$1.47 \$1.80 2 \$.30 \$.63 \$.96 \$1.29 \$1.62 \$1.95 3 \$.45 \$.78 \$1.11 \$1.44 \$1.77 4 \$.60 \$.93 \$1.26 \$1.59 \$1.92 5 \$.75 \$1.08 \$1.41 \$1.74 \$2.07 6 \$.90 \$1.23 \$1.56 \$1.89 7 \$1.05 \$1.38 \$1.71 \$2.04 8 \$1.20 \$1.53 \$1.86 9 \$1.35 \$1.68 \$2.01 10 \$1.50 \$1.83 11 \$1.65 \$1.98 12 \$1.80

Solution 4. Another way to approach the problem is to realize that using only 15¢ stamps makes the total end in 0 or 5. Next look at the number of 33¢ stamps that can be used to make a total that ends in either 2 or 7.

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