desperate for help maths prob -
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desperate for help maths prob -
In class , one third of the pupils bring a teddy bear to school. Last term, each boy took 12 books out of the library, each girl took 17 books and each teddy bear took 9 books. In total 305 books were taken out.
How many girls in class?
How many girls in class?
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Sorry - no idea.
I did:
Teddies = 1/3 (Girls+Boys)
305 = 12xboys + 17xGirls + 9xteddies
305 = 12B + 17G + 9x 1/3 (G+B)
305 = 15B + 20 G
then got stuck on the theory so trial and errored from there, remembering that G + B had to be a number devisable by 3.
Hopefully someone with less rusty maths than me can help.
I did:
Teddies = 1/3 (Girls+Boys)
305 = 12xboys + 17xGirls + 9xteddies
305 = 12B + 17G + 9x 1/3 (G+B)
305 = 15B + 20 G
then got stuck on the theory so trial and errored from there, remembering that G + B had to be a number devisable by 3.
Hopefully someone with less rusty maths than me can help.
This is a junior maths challenge question.
This is how they answer it:
Number of boys is b
girls = g
teddy bears = 1/3 of b+g
In total boys took out 12b books
girls took out 17g books
total yaken out by bears 9 x 1/3(b+g) = 3(b+g)
So 12b + 17g +3(b+g) = 305
15b + 20g = 305
3b + 4g = 61
There are 5 positive integer solutions of this but...
If 1/3 of b + g is a positive integer, then b = 11 and g=7
This is a diophantine equation.
This is how they answer it:
Number of boys is b
girls = g
teddy bears = 1/3 of b+g
In total boys took out 12b books
girls took out 17g books
total yaken out by bears 9 x 1/3(b+g) = 3(b+g)
So 12b + 17g +3(b+g) = 305
15b + 20g = 305
3b + 4g = 61
There are 5 positive integer solutions of this but...
If 1/3 of b + g is a positive integer, then b = 11 and g=7
This is a diophantine equation.