CHAPTER XXV.
Problems.
280. In previous chapters we have given collections of problems which lead to simple equations. We add here a few examples of somewhat greater difficulty.
Ex. 1. A grocer buys 15 lbs. of figs and 28 lbs. of currants for $2.60; by selling the figs at a loss of 10 per cent, and the currants at a gain of 30 per cent, he clears 30 cents on his outlay : how much per pound did he pay for each ?
Let x, y denote the number of cents in the price of a pound of figs and currants respectively; then the outlay is
15 X + 28 y cents. 15x + 28y = 260 (1).
The loss upon the figs is {1}{10} 15 x cents, and the gain upon the currants is {3}{10} x 28y cents; therefore the total gain is {42y}{5} - {3x}{2} cents; {42y}{5} - {3x}{2} = 30 (2).
From (1) and (2) we find that x = 8, and y = 5; that is, the figs cost 8 cents a pound, and the currants cost 5 cents a pound.
Ex. 2. At what time between 4 and 5 o'clock will the minute-hand of a watch be 13 minutes in advance of the hour-hand ?
Let x denote the required number of minutes after 4 o'clock ; then, as the minute-hand travels twelve times as fast as the hour-hand, the hour-hand will move over {x}{12} minute divisions in x minutes. At 4 o'clock the minute-hand is 20 divisions behind the hour-hand, and finally is 13 divisions in advance; therefore the minute-hand moves over 20 + 13, or 33 divisions more than the hour-hand.
