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Problems producing Simple Equations:

I divide 240 shillings among a certain number of boys, of whom, if there had been five more, each would have received 10s. How many boys are there?

Let x = No. of boys.
*+5=No. of boys in supposed case

240
and

=10s. X +5

240=10x + 50

10x=190:.x=19=No.of boys. 1. I divide 60 marbles among two boys, so that the one has four times as many as the other. How many has each ?

Let x=No. of one boy's share.

then 4x=other's.
And v + 4x=60:.«=12 and t=48.

Then a

2. Divide 33 yards of silk so that one part may be of the other.

x = greater part

lesser
2 + x

33
a = 2310 yds.

of 2310 = 18 = 91. yds. 3. What is that number which when trebled and added to 17 makes 97 ?

X = number
Then 3x+17 = 97

: 263 4. Two boys are within 7 years of each other, the one being as much above 17 as the other is below it. What are their ages ?

a = age of younger
Then x =

: 133 :: 131 +7 = 202 = the age of the elder. 5. If I had three times as many marbles as I have, and 17 more I should have 47, how many have I ?

X = number
Then 3x +17 = 47

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=

a = 10

= 24

a = 12

6. I am three times as old as my son; six years ago I was five times as old. What is my age ?

a = son's age
3x = father's age
3x—6 = 5 (2—6)
22

father's age = 36 7. It takes 75 yards of carpet for a room the breadth of which is 16 feet. What is its length ?

length 16x 225 feet

14 feet

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8. I divide 60 marbles among three boys, so that the first has twice as many as the second, and the second one three times as many as the third. How many had each ?

a = share of third Зr

second 6x

first x + 3x + 6x = 60

6 third's 3x = 18 second's

6x = 36 first's. 9. The sum of two numbers is 36 and their difference 2. What are the numbers ?

lesser number x + 2 = other number 2++2 =

= 36 a = 17

other number = 19 10. Divide 112 acres of land among two people, so that the one may have of the other's share.

Let x = one share

= other 2 +

112

877 112-87; 245 11. What number is that which is 24 more than its seventh part ?

a = number
X -- 24
7x - 2 = 168

X = 28 12. A certain number multiplied by 6, and the product lessened by 18, gives 3 times the original number. What is the number?

= number 6x-18

300

Then

X =

COW

13. A cow and sheep cost together £16; the cow cost 4į times as much as the sheep. What did each cost ?

Let x = cost of sheep
Then 4a
& +4

= £16
a = £3

£ (16-3) = £13 14. A man has five children, between each of whom there is a difference of six years, and the oldest is eight times as old as the youngest. What are their

ages

?
Let x = age of youngest
X+6

next

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& +12

9

@ +18 =
a + 24 =

eldest
*+24 = 8x =3.
i. Ans.

3, 94, 155,

214, and 27; 15. A man spends á of his income in rent, { in taxes, š in board, and saves £29 10s. What is his income per annum?

x = income

(70+45 +189) x 2. + 2+2=

=

315
3115x = £29 10s. x = £844 15s. 5 d.

304
315

=

16. A post is į of its length in water, õ in the soil, and 3 ft. 6 in. above the ground, what is the length of the post ?

length

(27+7) $+=

63 8 x + ft. 580 = 441 ft.

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75 ft.

17. I buy eggs at ls. 8d. per dozen; if I had bought six more for the same money, they would have cost twopence less. How many did 1 buy ?

= the number 1920 cost of one (+61 = 190 18x + 108 = 20x

2 = 54

PROBLEMS PRODUCING SIMPLE EQUATIONS. 1. A number consists of two digits, the unit's figure is twice as large as the ten's figure, and the sum of the digits is 6; what is the number? Ans. 24.

2. A father is 28 years older than his son, and their united ages are 64; what are the ages of father and son respectively? Ans. 18 and 46.

3. The sum and difference of two numbers is 16 and 2 respectively; what are the two numbers ? Ans. 7 and 9.

4. The sum of two numbers is 24, and their product 144; what are the numbers ? Ans. 12 & 12. 5. A

person has as many copper pennies as silver sixpences in his pocket; the total money he has is seven shillings; what number of each coin has he ? Ans. 12.

6. The product of two numbers is 132, and the quotient 11; what are the numbers ? Ans. 11 and 12.

7. Find what that number is which exceeds its sixth part by 60. Ans. 72.

8. A father is forty years old and bis son eight; in how many years will the father be three times as old as his son? Ans. 8 years.

9. Three men subscribe together three hundred pounds; the first subscribed three times as much as the third, and the second subscribed twice as much as the third; what did each subscribe ? Ans. £150, £100, and £50.

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