XI.

\$

22. -0.5$.

\$

23. -0.5$.

\$

24. -0.5$.

\$

25. -0.5$.

\$

26. -0.5$.

\$

To find $x$ in problem 26, add the equations; to find $y$, subtract one from the other. Do not clear of fractions.

157. Problems involving Two Unknown Numbers.

Ex. If A gives B $$10$, B will have three times as much money as A. If B gives A $$10$, A will have twice as much money as B. How much has each?

lint Let x = the number of dollars A has, lintand y = the number of dollars B has. [1] Then, after A gives B $$10,$ x - 10 = the number of dollars A has, y + 10 = the number of dollars B has. [1] Since B's money is now $3$ times A's, we have, y + 10 = 3(x - 10). (1) [1]

If B gives A $$10$, x + 10 = the number of dollars A has, y - 10 = the number of dollars B has. [1] Since A's money is now $2$ times B's, we have x + 10 = 2(y - 10). (2)

From the solution of equations (1) and (2), $x=22$, and $y=26$.

Therefore A has $$22$, and B has $$26$.

Exercise 66.

1. If A gives B $$200$, A will then have half as much money as B; but if B gives A $$200$, B will have one-third as much as A. How much has each?

2. Half the sum of two numbers is $20$, and three times their difference is $18$. Find the numbers.

3. The sum of two numbers is $36$, and their difference is equal to one-eighth of the smaller number increased by $2$. Find the numbers.