| AB = | R (A + B) |
| AB = | AR + BR |
| A B - BR = | AR |
| B (A - R) = | AR |
| AR | |
| B = | |
| A - R |
Similarly, if A is the missing counts of the two-fold yarn, the rule for A can be proved thus—
| AB = | R (A + B) |
| AB = | AR + BR |
| AB - AR = | BR |
| A (B - R) = | BR |
| BR | |
| A = | |
| B - R |
Examples in folded yarns.
Example 30.—Find the counts of 64's, 48's and 32's yarns folded together, and also give average when they are used separately one thread of each size in a garment. From the formula proved in Example 28 we have the following, taking the highest counts as starting-point—
| 64 hanks of 64's counts weigh | 1 | lb. |
| 64 hanks of 48's counts weigh | 1⅓ | lb. |
| 64 hanks of 32's counts weigh | 2 | lb. |
| 64 hanks folded yarn weigh | 4⅓ | lb. |
therefore—
| 64 | |
| = 1410⁄13 × 3 = 444⁄13 counts. | |
| 4⅓ |
In the hosiery trade such yarns are more often used separately than folded together, when the more useful problem is to find the average counts of the three threads which is obtained by multiplying this result by the number of threads in the set, in this case 3.
Average counts = 1410⁄13 × 3 = 444⁄13 average.