SOLUTION: Find the consecutive even numbers such that the sum of 3/5 of the first, 1/2 of the second and 3/8 of the third is 32.

Algebra ->  Equations -> SOLUTION: Find the consecutive even numbers such that the sum of 3/5 of the first, 1/2 of the second and 3/8 of the third is 32.      Log On


   



Question 1148560: Find the consecutive even numbers such that the sum of 3/5 of the first, 1/2 of the second and 3/8 of the third is 32.
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers be +n+, +n%2B2+, +n+%2B+4+
+%283%2F5%29%2An+%2B+%281%2F2%29%2A%28+n+%2B+2+%29+%2B+%283%2F8%29%2A%28+n+%2B+4+%29+=+32+
Multiply both sides by +40+
+24n+%2B+20%2A%28+n+%2B+2+%29+%2B+15%2A%28+n+%2B+4+%29+=+1280+
+24n+%2B+20n+%2B+40+%2B+15n+%2B+60+=+1280+
+59n+=+1180+
+n+=+20+
+n+%2B+2+=+22+
+n+%2B+4+=+24+
The numbers are 20, 22, and 24
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check:
+%283%2F5%29%2An+%2B+%281%2F2%29%2A%28+n+%2B+2+%29+%2B+%283%2F8%29%2A%28+n+%2B+4+%29+=+32+
+%283%2F5%29%2A20+%2B+%281%2F2%29%2A22+%2B+%283%2F8%29%2A24+=+32+
+12+%2B+11+%2B+9+=+32+
+32+=+32+
OK

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Presumably this problem is intended as an exercise in using algebra to solve problems. However, note that a little logical reasoning can get to the answer much faster, and with much less effort.

(1) Each of the fractions is close to 1/2; so the sum of the three numbers is about 2*32=64. So the three numbers are in the low 20s.

(2) 3/5 of the first number is a whole number, so the first number must be a multiple of 5. And since it is even, it must be a multiple of 10.

(3) A number in the low 20s that is a multiple of 10 has to be 20. So the three numbers are PROBABLY 20, 22, and 24.

CHECK:
(3/5)*20 + (1/2)*22 + (3/8)*24 = 12+11+9 = 32