Problem Solving Strategy ~ Guess and Check ~
 Solution

1. Mary has 6 coins, which have a total value of 67 cents. What combinations of coins could she have? Use denominations of 1¢, 5¢, 10¢ and 25¢.

 Penny 1¢ Nickel 5¢ Dime 10¢ Quarter 25¢ Total 2 1 1 2 6

2. Navigate your spaceship to the "Black Hole". The product of the numbers along your path must be 2592.

 Start 6 2 10 3 4 9 2 7 1 8 2 4 5 Black Hole

2 x 3 x 6 x 4 x 9 x 2 = 2592

3. The sums of numbers on each side of the magic triangle are all the same. Find two solutions for the magic triangle using a different number in each box.

 10
Sum = 10 + 24 + 16 = 50

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A + B = 40 & B + C = 32
 24
 A
Fix a number for B and the  will

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difference from the above sums
 16
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 C
------
 B
yield A and C

4. a) How many shots at this target are needed to make a score of 300?

b) Find four different combinations where the value of the shots on the target totals 300.

 Numbers 45 48 51 54 57 Total No. of shots 0 3 2 1 0 300 No. of shots 2 1 1 1 1 300 No. of shots 2 2 0 0 2 300 No. of shots 2 1 0 3 0 300

5. If r is less than 10, what value of r makes r3749r0 divisible by 60? (there are two possibilities.)

r3749r0 ÷ 60 ====> r3749r ÷ 6
A number divisible by 6 is even and divisible by 3.
So r must be even and r3749r is its divisibility by 3.

3 + 7 + 4 + 9 = 23

23 + r + r  is divisible by 3 and r < 10 and even

===> r = 2 and 8

6. Find a set of 3 consecutive even numbers whose sum is 294.

294 ÷ 3 = 98

 98 - 2 98 98 + 2 96 98 100