Maths Magic

Algebra Level 2

There are some coloured crayons in a box. The box contains R red colours, B blue colours and G green colours.

When I carry out the following steps-

{Multiply the number of red colours, R by 2, add 1, then multiply result by 5, add the number of blue colours, B, then multiply result by 10, add the number of green colours, G and then subtract 50 from result},

I get 869 as the final answer,

AND

The box contains no more than 9 crayons of a same colour (R<10, B<10, G<10)

Find the total number of crayons in that box, R+ B+ G= ?


The answer is 23.

Stuti Malik by Stuti Malik , 24, United Kingdom

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1 solution

Stuti Malik
Aug 25, 2015

(2R + 1)*5= 10R + 5

(10R +5 + B)* 10= 100R + 50 + 10B

100R + 50 + 10B + G - 50= 100R + 10B + G

(100)R + (10)B + G= 869

As it is now given that R, B and G are not more than 9 i.e. they are single digit numbers, it implies that:

R hundred + B tens + G= RBG= 869

So, R + B + G= 8 + 6 + 9= 23

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Why can't R = 8 , B = 5 , G = 19 R=8,B=5,G=19 be a solution? Or R = 7 , B = 105 , G = 19 R=7,B=105,G=19 ...

Janardhanan Sivaramakrishnan - 5 years, 9 months ago

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Yes, you are right, there are some alternative answers also possible. I should have mentioned one more condition such as the box does not contain more than 9 crayons of a same colour. Thank you, I will make that change.

Stuti Malik - 5 years, 9 months ago

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