Page:Elementary algebra (1896).djvu/179

161 Rh And from (1) 15 x + 350 = 1550.

Whence 15 x = 1200 ; x = 80.

Therefore the cost of a pound of tea is 80 cents, and the cost of a pound of coffee is 35 cents.

Ex. 3. A person spent $0.80 in buying oranges at the rate of 3 for 10 cents, and apples at 15 cents a dozen ; if he had bought five times as many oranges and a quarter of the number of apples, he would have spent $ 25.45. How many of each did he buy ?

Let x represent the number of oranges and y the number of apples.

x oranges cost {10x}{3} cents,

y apples cost {15y}{12}  cents ; {10x}{3} + {15y}{12}  = 680 (1)

Again, 5 x oranges cost 5 x {10}{3} , or  {50x}{3}  cents, and  {y}{4}  apples cost {y}{4} \times {15}{12}, or {15y}{48} cents;

{50x}{3} + {15y}{48} = 2545 (2).

Multiply (1) by 5 and subtract (2) from the result ; then ({75}{12} - {15}{48})y =855; or {285 y}{48 } = 855 ; y = 144;

and from (1) x = 150.

Thus there were 150 oranges and 144 apples.

Ex. 4. If the numerator of a fraction is increased by 2 and the denominator by 1, it equals {5}{8}  ; and if the numerator and denominator are each diminished by 1, it equals  {1}{2}: find the fraction.

Let x represent the numerator of the fraction, y the denominator; then the fraction is {x}{y}.

From the first supposition, {x+2}{y+1}  =  {5}{8}  (1)

from the second, {x-1}{y-1}  =  {1}{2}  (2)

These equations give x = 8, y = 15

Thus the fraction is {8}{15}.