Page 106 - Mathematics

Hence, x = 23. Simplifying simultaneous equations

Therefore, the larger number is 23 gives,
and the smaller number is 7.  pr+= 37,000
 p − 3r = 83,000
Example 5.40 
Use substitution method to solve
Dashi has 83,000 Tanzanian equations (i) and (ii) as follows.
shillings for shopping. If he buys From equation (ii), expressing p in
2 ties and 2 shirts, he remains with terms of r gives
9,000 Tanzanian shillings. If he
Tanzania Institute of Education
buys 1 tie and 3 shirts he spends p = 83000 3r− (iii)
all the money. Find the price of a Substitute equation (iii) into
tie and a shirt. equation (i), that is,

Solution 83000 3rr 34000
−
+=
Let: p be the price of a tie in 83000 2r− = 34000
Tanzanian shillings.
r be the price of a shirt in − 2r = − 46000
Tanzanian shillings. r = − 46000
− 2
It implies that for the first option, = 23,000
the cost for 2 ties is Tshs 2p and
the cost for 2 shirts is Tshs 2.r
Hence, r = 23,000

Thus, the total cost for 2 ties and 2 Substitute r = 23,000into equation
shirts is 2p + 2r. (iii) to obtain the value of p. That is
For the second option, the cost for p = 83,000 (3 23,000)− ×
1 tie is Tshs p and the cost for 3 = 83,000 69,000−
shirts is Tshs 3.r
= 14,000

Therefore, the total cost for 1 tie Therefore, the price of each tie is
Mathematics Form One From this information, form a Tanzanian shillings.
14,000 Tanzanian shillings and
and 3 shirts is p + 3r.
the price of each shirt is 23,000
system of linear simultaneous
equations as follows:
2 ) 9 000r =
83 000 (2p−
+


+
83 000 (p−
3 ) 0r =

100

25/10/2024 09:51:35
Mathematics form 1.indd 100 25/10/2024 09:51:35
Mathematics form 1.indd 100