192. (3x+7) (2 x + 1) − (5 x+3)=14x-2. 193. 8y+1- [4 y − 1 − (3 y − 1)] = 0.

194. 5(x+2)+2(x − 3) = 4 (x − 5) — 2 (x + 1).
195. (y+1)2 - (y + 2)2 = (y+3)2 — (y + 5)2.
196. (x+3)(x+4) − (x + 2) (x + 1) — 30 = 0.
197. 2(y+1)(y+2)-2 (y-1) (y — 2) = 36.
198. 3x(x+1)- 2 x (x + 1) − x (x+6) = 21.

199. 3 y (y-1) — 3 (y + 1) (y − 1) = 4 (y — 3).

200. 5 x (x −4) — 7 x (x − 5) + 2 x (x + 6) = 15.

201. (4 y-1) — (2 y − 1)2 — (2 y + 1)2 — 8 y2 − 2 =0.

202. (3x+1)2 - 4 z (z+3) — 5 z (z − 3) = 0.

203. (2x+1)(3 x + 1) − (4 x + 1) (2 x − 1) = (4 + x) (1 − 2 x).

204. 3x2(x+1)- 3 x2 (x − 1) — 6 x (x + 1) − 1 = 0.

205. 5(y+1)− 5 [y − (y + 1)] − 5 [2 y − 3 (y + 1)] = 0.

206. (x+1)3 — (x − 1)3 − 6 (x + 1) (x − 1) = x.

207. (4x+3)(2 x + 1)(x + 1) −4 (2x+1)(x+1)(x−1)=14x2.

Problems leading to Linear Equations

State and solve:

208. Find five consecutive numbers whose sum is 115. 209. Find five consecutive even numbers whose sum is 210. 210. Find seven consecutive odd numbers whose sum is 245. 211. Find two numbers whose sum is 70, and whose difference is 6.

212. Divide 125 into two parts, one of which is 43 more than the other.

213. Divide $1400 between A and B, so that A shall re ceive $230 more than B.

214. Divide 120 into four parts, each of which shall be 10 more than the next smaller part.

215. A and B together have $390, and A has $90 more than B. How many dollars has each ?

216. The difference between the squares of two consecutive even numbers is 52. What are the numbers?

217. The sum of

two numbers is 16, and the difference of their squares is 32. What are the numbers ?

218. Divide 70 into two parts, such that ten times the smaller part shall equal eight times the larger part.

219. Divide 31 into two parts such that 1 less than 8 times the smaller shall equal 5 times the larger part.

220. Ten times a certain number is as much above 77 as 43 is above five times the number. What is the number?

221. How can you pay a bill of $5.95 with the same number of coins of each kind, using only dimes and quarters ?

222. A man divided $1500 among four sons, each receiving $50 more than the next youngest. What amount did each receive?

223. A, B, and C together have $213. C has twice as much as A, and $57 more than B. How many dollars has each?

224. A certain number exceeds another number by 3, and the difference between their squares is 51. What are the numbers?

225. A boy has $2.25 in dimes and nickels, and has the same number of coins of each kind. How many coins has he in all ?

226. Divide one dollar between two boys so that one of them shall receive 10 cents more than twice the amount the other receives.

227. A certain man is three times as old as his son, and in

years the sum of their ages is 66 years. What is the age of

5
each now?

228. Divide 74 into three parts such that the second shall be 6 more than the first, and the third 10 less than the second part.

5

229. The combined ages of two brothers is 50 years, and in years the older will be twice as old as the younger. How old is each now?

230. The sum of the ages of a father and son is 80 years, and twice the son's age exceeds the father's age by 1 year. Find the age of each.

231. The distance around a rectangular hall is 720 feet, and the length of the hall is double its width. Find the dimensions of the room.

232. A baseball team played 140 games in a season, winning 42 more games than it lost. What was the number of games won?

233. Two workmen receive together $45 for a certain task, and one receives twice as much as the other. What amount does each receive?

234. One number is three times another, and if the smaller is subtracted from 34, and the larger subtracted from 70, the remainders are equal. Find the numbers.

235. The annual salaries of A and B together amount to $6700, and A receives $100 more than twice the amount B receives. Find the annual salary of each.

236. The sum of the ages of a father and son is 96 years, but if the son's age is trebled, it will be 8 years greater than the father's age. What is the age of each?

237. There are three numbers, the third being 21 more than the second, while the first is 5 times the second and also 4 times the third. What are the numbers?

238. The oldest of three boys weighs twice as much as the youngest, and 15 pounds more than the second boy. If all three together weigh 335 pounds, what is the weight of each ?

239. A boy has two dollars in quarters, dimes, and nickels. He has 3 times as many dimes as quarters, and 3 times as many nickels as dimes. How many coins has he of each kind?

240. A bookcase, a table, and a chair together cost $77. The bookcase cost 7 times as much as the chair, and $13 more than the table. What was the cost of each?

241. In a certain high school class of 42 students the number of girls is 2 less than three times the number of boys. How many boys and how many girls are there in the class?

242. One number is three times another number, and the remainder when the smaller is subtracted from 19 is the same as the remainder when the larger is subtracted from 43. Find the numbers.

243. The total number in attendance at a church fair was 285, and 3 times the number of adults present equaled twice the number of children. How many adults and how many children attended?

244. After giving 14 cents to each of a group of boys I had 5 cents left, and I found that if I had given each boy 16 cents I would have lacked 5 cents of the necessary amount. How many boys were there?

245. In a certain family the father is 7 years older than the mother, and the sum of their ages is 9 times the age of their son. The combined ages of all three is 70 years. How

old is each?

246. A walks over a certain road at the rate of 3 miles an hour. Two hours after he leaves, B walks after him at a rate of 4 miles an hour. How many miles will A have gone when B overtakes him?

247. Three men, A, B, and C, are paid all together $7200, annually, and the difference between A's and B's salaries, and

also between B's and C's is $800. Find the amount that each receives annually.

248. Three people observe that the sum of their ages is 85 years, that the oldest is three times as old as the youngest, and that he is 20 years older than the second. How old is each?

249. A field of 30 acres is planted to corn and to wheat. Four times the number of acres planted to wheat equals six times the number planted to corn. How many acres are planted to each grain?

250. A and B are 60 miles apart, and start to travel toward each other. They leave at the same time, A going 4 miles an hour, and B going 5 miles an hour. In how many hours wi!'

they meet?

251. Two farms together cost $9600. For one of them a price of $70 an acre was paid, and for the other the price was $80 an acre. Both farms together contain 130 acres. How many acres are there in each?

252. Two automobiles start at the same time from towns 70 miles apart, and go toward each other. One goes at the rate of 20 miles, the other at the rate of 15 miles per hour. In how many hours will they meet?

253. $75.60 was taken at the gate at a ball game. Adults paid 50 cents each, and children 20 cents each, for admission. If 5 times as many adults as children attended the game, what number of each attended?

254. Two automobiles start at the same time from the same town and travel in opposite directions. One of them goes 20 miles an hour and the other 15 miles an hour. After how many hours will they be 70 miles apart?

255. A man has 3 hours at his disposal and walks out into the country at a rate of 4 miles an hour. How many miles may he walk so that, returning on a trolley car running 12 miles an hour, he will return in just 3 hours?