# New School Algebra

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1901 edition. Excerpt: ... alone to do the work? Let x, y, z = the number of days in which A, B, C can do the work, respectively. Then, -, -, -= the parts A, B, C can do in 1 day, respectively. x y z And-]-= the part A and B together can do in one day. But i = the part A and B together can do in 1 day. Therefore, -+-= 5' (1) 111 2Q Add, and divide by 2, -+-+-=-(4) Subtract (1), (2), and (3), separately from (4), and we have i-A 1--11 1 _ 13 z 72' y-72' x-72 ' Therefore, 2 = 142, y = 6fi, x = 6. Therefore, A can do the work in 5fa days, B in 6TeT days, and C in 14 days. 25. A cistern has three pipes, A, B, and C. A and B will fill the cistern in 1 hour 10 minutes, A and C in 1 hour 24 minutes, B and C in 2 hours 20 minutes. How long will it take each pipe alone to fill it? 26. A and B can do a piece of work in 2 days, A and C in 3j days, B and C in 4 days. How long will it take each alone to do the work? 27. A and B can do a piece of work in a days, A and C in b days, B and C in c days. How long will it take each alone to do the work? 28. A sum of money, at simple interest, amounted to \$2480 in 4 years, and to \$2600 in 5 years. Find the sum / and the rate of interest. Let x = the number of dollars in the principal, and y = the rate of interest. y v The interest for one year is r-rr of the principal, = rrr of x; for 4 years, =--of x; and for 5 years, =--of x. The amount is principal + interest. Therefore, x + = 2480., + = 2600. Hence, 100 x + 4 xy = 248,000. (1) 100 x + 5xy = 260,000. (2) Multiply (1) by 5 and (2) by 4, and we have 600 X + 20x = 1,240,000 400 x + 20 xy = 1,040,000 Subtract, 100 x = 200,000. Therefore, z = 2000. Substitute the value of x in (1), y = 6. Therefore, the sum is \$2000, and the rate 6%. 29. A sum of money, at simple interest, ...