Question 1120155: A Postmaster sells stamps usually in the proportion of fifteen 5 - centavo stamps to every six 6- centavo stamps and to every four 30 - centavo stamps in ordering 15,000 of these stamps, how many more 5 - centavo than 6 - centavo stamps should be ordered?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
Answer by ikleyn(52814)  (Show Source):
You can put this solution on YOUR website! .
An equivalent re-phrasing is that you can group the stamps sold in sets containing (15 of 5-centavo + 6 of 6-centavo + 4 of 30-centavo) stamps.
Each group contains 15+6+4 = 25 stamps.
15000 stamps contain  = 600 such groups, i.e. contain
15*600 of 5-centavo
6*600 of 6-centavo
4*600 of 30-centavo stamps.
Now the number under the question is 15*600 - 6*600 = 9*600 = 5400.
Answer. The number under the question is 5400 stamps.
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