PROBLEMS INVOLVING THREE OR MORE UNKNOWN QUANTITIES 241. In solving problems which involve two or more unknown quantities, the pupil should first discover from the statement of the problem the number of quantities which are to be determined. When he has learned this fact, he must then obtain from the conditions of the problem, as many equations connecting the unknown quantities as there are unknown quantities to be determined. The unknown quantities can now be found by solving the equations (238). 242. PROBLEM I. Find the numbers which are in the ratio 234, and whose sum is 999. Let x, y, z be respectively the first, second, and third of the required numbers. Hence, according to the first condition of the PROBLEM II. A lent his money at 4%, B at 5%, C at 6%. How much money had each, if A and B received together $1592 interest, B and C together $1766 interest, A and C together $1638 interest? Then Let x, y, and z be respectively the capital of A, B, and C. the interest which each received will be respectively the following: Hence, according to the conditions of the problem, PROBLEM III. A miner has three ingots composed of gold, silver, and copper, which contain respectively: the first, 50 gr. of gold, 60 gr. of silver, 80 gr. of copper; the second, 30 gr. of gold, 50 gr. of silver, 70 gr. of copper; the third, 35 gr. of gold, 65 gr. of silver, 90 gr. of copper. What weight should be taken from each ingot in order to form an ingot containing 79 gr. of gold, 118 gr. of silver, and 162 gr. of copper? Let x, y, z be respectively the weights taken from each of the three ingots. The first ingot contains 50 +60 + 80, or 190 gr., of which 50 gr. is gold, 60 gr. silver, and 80 gr. copper; therefore in the composi |