SOLUTION: The number of lemons a fruit seller bought in December was 30% more than in November. In January, he bought 50% less lemons than in December. If there were 3577 more lemons in Nove
Question 1192503: The number of lemons a fruit seller bought in December was 30% more than in November. In January, he bought 50% less lemons than in December. If there were 3577 more lemons in November than January, how many lemons did the fruit seller buy in November? Found 2 solutions by Theo, greenestamps:Answer by Theo(13342) (Show Source):
d = n + .3 * n = 1.3 * n
j = d - .5 * d = .5 * d
n = j + 3577
d = the number of melons bought in december.
j = the number of melons bought in january.
n = the number of melons bought in november.
since n = j + 3577 and j = .5 * d and d = 1.3 * n, then:
n = .5 * 1.3 * n + 3577
combine like terms to get:
n = .65 * n + 3577
subtract .65 * n from both sides of the equqtion to get:
.35 * n = 3577
solve for n to get:
n = 3577 / .35 = 10220.
since n = j + 3577, then j = n - 3577 = 10220 - 3577 = 6643.
since d = 1.3 * n, then d = 1.3 * 10220 = 13286.
you have:
d = 13286
j = 6643
n = 10220
d = 1.3 * n becomes 13286 = 1.3 * 10220 which becomes 13286 = 13286.
j = .5 * d becomes 6643 = .5 * 13286 which becomes 6643 = 6643.
n = j + 3577 becomes 10220 = 6643 + 3577 which becomes 10220 = 10220.
if the assumption are correct, then the solution is correct.
the solution is that the fruit seller bought 10220 lemons in november.
x = # bought in November
1.30(x) = 1.3x = # bought in December (30% more then November)
.50(1.3x) = 0.65x = # bought in January (50% less than in December -- i.e., 50% as many)
The number bought in November is 3577 more than in January:
