Algebraic exercises

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Página 69 - SIXTH CLASSES. 1. Prove that in the multiplication of decimals, there are as many decimal places in the product as in the multiplier and multiplicand together. 2. Find two numbers, such that if % of the less be added to -\ of the greater, the sum will be 7; but if j of the greater be taken from the less, the remainder will be 2.
Página 71 - B. set out at the same time, and met each other, after travelling as many days as are equal to the difference of the number of miles they travelled per day ; when 'it appears that A has travelled 216 miles. How many miles did each travel per day ? Ans. A went 36, and B 30.
Página 47 - The number to be divided is called the dividend. The number by which we divide is called the divisor. The number which shows how many times the divisor is contained in the dividend is called the quotient.
Página 72 - It is required to divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5. Ans. 20 and 40 6.
Página 68 - To find a number consisting of three places, whose digits are in arithmetical progression; if this number be divided by the sum of its digits, the quotient will be 48 ; and if from the number be subtracted 198, the digits will be inverted.
Página 81 - Find a number consisting of three digits, such, that the sum of the squares of the digits, without considering their position, may be 104 ; but the square of the middle digit exceeds twice the product of the other two by 4 ; farther, if 594 be subtracted from the number sought, the three digits are inverted.
Página 64 - OD condition of having a farthing for the first nail in his shoes, a halfpenny for the second, a penny for the third, twopence for the fourth, and so on, doubling the price of every nail, to 32, the number of nails in his four shoes ; what would the horse be sold for at that rate ? Ans.
Página 81 - What two numbers are they, whose difference is 8, and the sum of whose squares is 544? Ans. 12 and 20 ; or — 12 and —20.
Página 72 - Ans. 18 and 6. 13. In a mixture of rum and brandy, the difference between the quantities of each, is to the quantity of brandy, as 100 is to the number of gallons of rum ; and the same difference is to the quantity of rum, as 4 to the number of gallons of brandy.

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