Question 1120155
he sells 15 five centavo stamps for every 6 six centavo stamps and every 4 thirty centavo stamps.


let x represent the number of five centavo stamps.
let y represent the number of six centavo stamps.
let z represent the number of thirty centavo stamps.


the ratio of five centavo stamps to six centavo stamps is 15/6, therefore:


x/y = 15/6
cross multiply to get 6x = 15y
solve for y to get y = 6x/15.


the ratio of five centavo stamps to thirty centavo stamps is 15/4, therefore:


x/z = 15/4
cross multiply to get 4x = 15z
solve for z to get z = 4x/15


you have:


x = x
y = 6x/15
z = 4x/15


since he bought a total of 15000 stamps, then:


x + y + z = 15000


replace y with 6x/15 and z with 4x/15 to get:


x + 6x/15 + 4x/15 = 15000


multiply both sides of this equation by 15 to get:


15x + 6x + 4x = 15000 * 15


combine like terms to get:


25x = 15000 * 15


divide both sides of this equation by 25 to get:


x = 15000 * 15 / 25


solve for x to get:


x = 9000


since y = 6x/15, then y = 6*9000/15 = 3600


since z = 4x/15, then z = 4*9000/15 = 2400.


x + y + z = 15000 becomes 9000 + 3600 + 2400 = 15000 which becomes 15000 = 15000 which is true.


x/y = 9000/3600 = 2.5 and 15/6 = 2.5, therefore 9000/3600 = 15/6.


x/z = 9000/2400 = 3.75 and 15/4 = 3.75, therefore 9000/2400 = 15/4.


the solution looks good when x = 9000 and y = 3600 and z = 2400.


that means he should buy 9000 five centavo stamps and 3600 six centavo stamps and 2400 thirty centavo stamps.


9000 minus 3600 = 5400.


therefore, he should buy 5400 more five centavo stamps than six centavo stamps is your solution.