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Form 1 Mathematics Linear Equations Questions and Answers
Simplify the expression
x
-
1
x
-
2
x
+
1
3
x
Hence solve the equation
x
-
1
x
-
2
x
+
1
3
x
=
2
3
(2m 13s)
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1.
Three artisans and two craftsmen earn sh. 220 in a day while four artisans and one craftsman earn sh. 185. Find the amount of money a craftsman earns in a day.
2.
A shopkeeper bought 50 pangas and 30 jembes from a wholesaler A for sh. 4,260. Had he bought half as many jembes and 5 pangas less, he would have paid sh. 1,290 less. Had the shopkeeper bought from wholesaler B, he would have paid 10 % more for a panga and 15% less for a jembe. How much would he have saved if he had bought the 50 pangas and the 30 jembes from wholesaler B.
3.
The total weekly wages for 12 artisans and 4 apprentices are sh. 5, 600. If the number of artisans is increased to 15 and that of the apprentices to 9, the total weekly wages are sh. 7,800. Calculate the weekly wage for an artisan.
4.
Two pairs of trousers and three shirts cost a total of sh.390. Five such pairs of trousers and two shirts cost a total of sh. 810. Find the price of a pair of trousers and a shirt.
5.
Solve the equation
1
4
x
=
5
6
x
-
7
6.
Given that x = -2, find the values of y and z for the simultaneous equations. x + y-z = -1, x -2y+ z = -7
7.
Three years ago Juma was three times as old as Ali. In two years time the sum of their ages will be 62. Determine their present ages.
8.
A shopkeeper sells two types of pangas, type x and type y. Twelve type x pangas and five type y pangas cost sh 1,260, while nine type x pangas and fifteen type y pangas cost sh 1,620. Mugala bought eighteen type y pangas. How much did he pay for them?
9.
The cost of 5 skirts and 3 blouses is sh 1,750. Mueni bought three of the skirts and one of the blouses for sh. 850. Find the cost of each item.
10.
A fruiterer bought 144 pineapples at sh. 100 for every six pineapples. She sold some of them at sh. 72 for every three and the rest at sh. 60 for every two. If she made a 65% profit, calculate the number of pineapples sold at sh. 72 for every three.
11.
Four farmers took their goats to the market. Mohammed had two more goats than Ali. Koech had 3 times as many goats as Mohammed, whereas Odupoy had 10 goats less than both Mohammed and Koech. (i) Write a simplified algebraic expression with one variable, representing the total number of goats. (ii) Three butchers bought all the goats and shared them equally. If each butcher got 17 goats, how man
12.
Akinyi bought three cups and four spoons for sh. 324. Wanjiku bought five cups and Fatuma bought two spoons of the same type as those bought by Akinyi. Wanjiku paid sh 228 more than Fatuma. Find the price of each cup and each spoon.
13.
Mary has 21 coins whose total value is sh. 72. There are twice as many five coins as there are ten shilling coins. The rest are one shilling coins. Find the number of ten shilling coins that Mary has.
14.
The mass of 6 similar art books and 4 similar biology books is 7.2kg. The mass of 2 such art books and 3 such biology books is 3.4 kg. Find the mass of one art book and the mass of one biology book.
15.
Simplify the expression
x
-
1
x
-
2
x
+
1
3
x
Hence solve the equation
x
-
1
x
-
2
x
+
1
3
x
=
2
3
16.
Karani bought 4 pencils and 6 biro-pens for sh.66 and Tachora bought 2 pencils and 5 biro-pens for sh 51. (a) Find the price of each item. (b) Musoma spent sh. 228 to buy the same type of pencils and biro-pens. If the number of biro-pens he bought were 4 more than the number of pencils, find the number of pencils he bought.
17.
(a) Write an expression in terms of x and y for the total value of a two digit number having x as the tens digit and y as the units digit. (b) The number in (a) above is such that three times the sum of its digits is less than the value of the number by 8. When the digits are reversed the value of the number increases by 9. Find the number.
18.
Hadija and Kagendo bought the same types of pens and exercise books from the same shop. Hadija bought 2 pens and 3 exercise books for sh 78. Kagendo bought 3 pens and 4 exercise books for sh 108. Calculate the cost of each item.
19.
In fourteen years time, a mother will be twice as old as her son. Four years ago, the sum of their ages was 30 years. Find how the old the mother was, when the son was born
20.
In January, Mambo donated
1
6
th of his salary to a children’s home while Simba donated
1
5
th of his salary to the same children’s home. Their total donation for January was Ksh 14820. In February, Mambo donated
1
8
th of his salary to the children’s home while Simba donated
1
12
th of his salary to the children’s home. Their total donation for February was
21.
Bukra had two bags A and B, containing sugar. If he removed 4 kg of sugar from bag A and added it to bag B, the mass of sugar in bag B would be four times the mass of sugar in bag A. If he added 10kg of sugar to the original amount of sugar in each bag, the mass of sugar in bag B would be twice the mass of sugar in bag A. Calculate the original mass of sugar in each bag.
22.
The cost of 2 jackets and 3 shirts was Ksh 1 800. After the cost of a jacket and that of a shirt were increased by 20%, the cost of 6 jackets and 2 shirts was Ksh 4 800. Calculate the new cost of a jacket and that of a shirt.
23.
A construction company employs technicians and artisans. On a certain day 3 technicians and 2 artisans were hired and paid a total of Ksh 9000. On another day the firm hired 4 technicians and 1 artisan and paid a total of Ksh 9500. Calculate the cost of hiring 2 technicians and 5 artisans in a day.
24.
A two digit number is such that, the sum of its digits is 13. When the digits are interchanged, the original number is increased by 9. Find the original number.
25.
Expand and simplify: 4(q+6)+7(q-3)
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