Katie had a
collection of red, green and blue beads. She noticed that the number of beads
of each colour was a prime number and that the numbers were all different.
She also observed that if she multiplied the number of red beads by the total number of
red and green beads she obtained a number exactly 120 greater than the number
of blue beads.
How many beads of each colour did she have?
SOURCE: Scottish Mathematical Challenge.
If R is 2 then B=2 which isn't allowed.
B can't be 2 because the only factors of 122 are 2*61.
So R and B are odd, RHS is odd, and (R+G) must be odd, making G=2.
Then (R-10)(R+12)=B, R=11 and B=23.
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Posted by xdog
on 2018-03-21 07:55:40 |
solution
