Question

A bag contains purple marbles and white marbles, 42 in total. The number of purple

marbles is 7 more than 4 times the number of white marbles. How many purple
marbles are there?

Answer 1

k=7

Explanation:

Pythagoras: a^2+b^2=c^2

5^2+x^2=k^2

25+x^2=49

x^2=24

x~4.899

C(x) = 1000(8 - x) + 2000k + 25

=8000-1000x+14000+25

=22000-1000x+25~17101+25

so it's option D

Answer 2

35

Explanation:

let x be the number of white marbles and y be the number of purple marbles

this implies that,

y = 42-x

also y = 7+4x

equate the two equations for y

42-x = 7+4x

collect like terms

42-7 = 4x +x

35 = 5x

divide both sides by the coefficient of x which is 5

35/5 = 5x/5

x = 7

substitute the value of x into the first equation

y = 42-x = 42- 7 = 35

there are 35 purple marbles.