Ratio & Proportion

• Jun 12th 2008, 07:41 AM
MathLearner
Ratio & Proportion
Two barrels A and C contain alcohol nd water in the ratio 1:a and 1:c respectively. Equal quantities of the mixtures from the two barrels are mixed to get a mixture with alcohol and water in the ratio 1:b , where b is the arithmetic mean of a and c. what can be the value of a+b+c if all three are integers ?
• Jun 12th 2008, 07:50 AM
colby2152
Quote:

Originally Posted by MathLearner
Two barrels A and C contain alcohol and water in the ratio 1:a and 1:c respectively. Equal quantities of the mixtures from the two barrels are mixed to get a mixture with alcohol and water in the ratio 1:b , where b is the arithmetic mean of a and c. what can be the value of a+b+c if all three are integers ?

BARREL - ALCOHOL - WATER
A - 1 - a
C - 1 - c

$\displaystyle b = \frac{a+c}{2}$

a and c can be anything, but they must both be odd or both be even so that b is an integer.
• Jun 12th 2008, 07:54 AM
MathLearner
The options given for this problem re 14,10,15 & 8. Which is the right one nd what can be the individual values of a & b ?
• Jun 12th 2008, 08:03 AM
colby2152
Quote:

Originally Posted by MathLearner
The options given for this problem re 14,10,15 & 8. Which is the right one nd what can be the individual values of a & b ?

The number must be of the form: $\displaystyle n = 1.5x$

Only one number satisfies that equation where x and n are integers.