Brain Teasers
Beads
Juliet bought 10 beads for
$18. The beads she bought are red, blue or silver. Red beads are $1 each, blue
beads are $2 each and silver beads are $5 each.
If she bought at least one of each, how many red beads did she buy?
Puzzle provided by Noetic Learning Math
Contest
Solution: 5 red beads.
If Julie bought 2 silver beads, she would only have $8 left
to purchase 8 more beads. In that case, she would not be able to buy any blue
beads. So, Julie can only purchase 1 silver bead.
That leaves her $18-$5=$13 for 10-1= 9 beads (in red or
blue). We will use guess and check to
find the number of blue beads and red beads she bought.
Guess #1: 3 red beads and 6 blue beads
Check: the cost is $3
+ $12 = $15 > $13. Since a red bead costs less than a blue bead, we need to
increase the guess on the number of red beads.
Guess #2: 6 red beads and 3 blue beads
Check: the cost is $6
+ $6 = $12 < $13. Since a red bead
costs less than a blue bead, we need to decrease the guess on the number of red
beads.
Guess #3: 5 red beads and 4 blue beads
Check: the cost is $5
+ $8 = $13. That’s it! This is the answer we are looking for.
Therefore, Julie bought 1 silver bead, 4 blue beads, and 5
red beads.
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