98. Find the cost of 77 quarts of cherries, at 9 cents a quart. 99. Find the cost of 92 brooms, at 21 cents apiece. 100. Find the cost of 21 hats, at $1.87 apiece. 101. Find the cost of 18 cords of wood, at $4.75 a cord. 102. Find the cost of 81 cords of wood, at $7.45 a cord. 103. Find the cost of 74 acres of ground, at $37.50 an acre. 104. Find the cost of 12 farms, at $1127.91 apiece. 105. Find the cost of 27 suits of clothes, at $11.25 apiece. 106. Find the cost of 72 overcoats, at $17.25 apiece. 107. Mr. A travels at the rate of 12 miles in 2 hours, and Mr. B travels at the rate of 15 miles in 5 hours. How many miles does A gain on B in 1 hour? 108. If A and B should travel at these rates for 10 hours, how much farther would A go than B? 109. In the above example, the rates of travel remaining the same, how long would it take A to overtake B, who is 60 miles ahead? 110. If one of two trains has 100 miles the start, and moves at the rate of 15 miles an hour, how long will a second train, running at the rate of 25 miles an hour, be in overtaking it? . 111. A man divided 117 cents among 9 boys, giving to each the same number of cents; how many cents did each boy get? 112. A man divided 192 marbles among a certain lot of boys, giving to each boy the same number of marbles; how many boys were there? 113. Find the number of cents required to pay 18 boys, if each boy is paid 18 cents. 114. If 17 men are paid $187 for working a certain number of days, how many days did they work? 115. How much can 28 men earn in 29 days, at $4 per day? In what time can 7 boys earn the same amount at $2 per day? 116. At the rate of $51 for 17 days, in how many days can 3 men earn $81? 117. At the rate of $42 for 14 days, how many men can earn $96 in two days? 118. How many men can earn $192 in 7 days, if 7 men earn $14 in 2 days? Suggestion. By the last condition, how much does 1 man earn in 2 days? How much in one day? Then, by the first condition, how much does 1 man earn in 7 days? Finally, how many men will be required to earn $192 in 7 days? 119. If 1 man can carn $4 in one week, how many dollars can he earn in 10 weeks? 120. If $1 earns 4 cents in one year, how many cents will it earn in 10 years? 121. If the use of $1 for one year is worth five cents, how many cents is its use worth for 10 years? 122. If the interest on $1 for one year is 6 cents, what is the interest on $1 for 10 years? 123. If one man earns $5 in 1 week, how many dollars can 6 men earn in 10 weeks? 124. If $1 earns 6 cents in one year, how many cents will $6 earn in 10 years? 125. If the use of $1 for one year is worth 8 cents, how many cents is the use of $12 worth for 12 years? 126. If the interest on $1 for one year is 8 cents, what is the interest on $12 for 12 years? 127. Six men earn $12 in 1 week; how much does one man earn in one week? How much in 3 weeks? How much do 3 men earn in one week? How much do 3 men earn in 4 weeks? 128. If $6 earn 12 cents in one year, how many cents does $1 earn in one year? How many cents in 3 years? How many cents do $5 earn in one year? How many cents do $5 earn in 12 years? 129. If the use of $6 for one year is worth 12 cents, how many cents is the use of $18 worth for one year? How many cents is the use of $18 worth for 12 years? 130. Find the interest on $20 for 5 years, if the interest on $7 for 3 years is 84 cents. 131. How long will it take 5 men to earn $40, if 1 man can earn $2 in 1 day? 132. In how many years will $5 earn 40 cents, if $1 earns 2 cents in one year? 133. In how many years will $7 earn 21 cents, if $1 earns 3 cents in one year? 134. In how many days can 7 men earn $84, if 3 men earn $24 in 2 days? 135. In how many years will $7 earn 84 cents, if $3 earn 24 cents in 2 years? 136. Find the Greatest Common Divisor of 1728, 1844, and 2026. 137. Find the Least Common Multiple of 108, 208, 828, and 882, by factoring. 138. Find the Least Common Multiple of 8, 12, 15, 18, 21, 27, 32, 42, 51, and 91. 139. If you multiply any number by 4, and then divide the product thus found by 2, will the result be greater, or less, than the original number? 140. If you multiply any number by 8, and divide the product thus found by 7, will the result be greater, or less, than the original number? 141. Find the cost of 32 dozen eggs, at 12 cents a dozen. 142. Find the cost of 42 arithmetics, at 163 cents apiece. 143. Find the cost of 112 arithmetics, at 163 cents apiece. 144. Find the cost of 10 grammars, at 20 cents apiece. 145. Find the cost of 12 grammars, at 25 cents apiece. 146. Find the cost of 30 philosophies, at 33 cents apiece. 147. Find the cost of 88 horses, at $125 a head. 148. Find the cost of 64 horses, at $125 a head. Use cancellation in the following: 149. Multiply 24, 36, 48, and divide by 18 X 12 × 6. 150. Divide 56 X 65 X 81 by 27 X 13 X 8 X 5. 151. Divide 100 X 96 X 84 X 48 by 24 X 14 X 16 X 25. 152. Divide 250 X 1000 × 125 by 8 × 40 × 50. COMMON FRACTIONS. 101. A unit or any single thing, or several units considered as a single thing, may be divided into any number of equal parts. 102. When any thing is divided into two equal parts, each part is one-half of the whole thing, and is called a fractional part of the whole. This fraction is expressed thus: . The whole thing thus divided is expressed thus: 2, which is equal to 1 unit. 1 How many halves are there in 1 unit? How many halves are there in 10 units? 103. When any thing is divided into three equal parts, each part is one-third of the whole thing, and two of these equal parts are two-thirds of the whole thing. These fractions are expressed thus:,. The whole thing thus divided is written thus:, which is equal to 1 unit. How many thirds are there in 1 unit? How many thirds are there in 10 units? 104. When any thing is divided into four equal parts, each part is one-fourth of the whole thing. Two of these equal parts are two-fourths of the whole thing. Three of these equal parts are three-fourths of the whole thing. |