Page 154 - ArithBook5thEd ~ BCC

Neither the terms nor the solution of a proportion are necessarily whole numbers.

Example 192. Solve the proportion
10 15
=
B 4
for B and check the solution.

Solution. Setting the cross products equal,

40 = 15B.

Dividing both sides of the equation by 15 (the number multiplying B), and simplifying, yields

✚❃
✚ 40 8 = 15B
✚❃
✚ 15 3 15
8
= B.
3
2
The unknown term is 8 3 or 2 .
3
2
Substituting 2 for B in the original proportion, we check that the cross-products are equal.
3
" #
? 2
10(4) = 2 (15)
3
✚❃
? 8 ✚ 15 5
40 = 1
✚ 3 ✚❃ 1
40 = 40.

Example 193. Solve the proportion
2 x
, -
3 = .
5 15
Solution. Set the cross-products equal, and solve for x:
2
· 15 = 5x
3
5
2 · ✚ 15 = 5x
✚❃
✚ 3 ✚❃ 1
10 = 5x
2= x.

Example 194. Solve the proportion
42 x
= .
70 1.5

Page 154