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}.
