Page 107 - Mathematics_F1

Hence, x = 23. Simplifying simultaneous equations
Therefore, the larger number is 23 gives,
and the smaller number is 7.
pr = ) 37000
+ 
 3 ) 83000r =
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Example 5.39  p −
Use substitution method to solve
Dashi has 83,000 Tanzanian equations (1) and (2) as follows.
shillings for shopping. If he buys From equation (2), 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
all the money. Find the price of a p = 83000 3r− (3)
tie and a shirt. Substitute equation (3) into
equation (1), that is,
Solution
Let: p be the price of a tie in 83000 3rr 34000
+=
−
Tanzanian shillings. 83000 2r− = 34000
r be the price of a shirt in − 2r = − 46000
Tanzanian shillings. − 46000
r =
It implies that for the first option, − 2
the cost for 2 ties is Tshs 2p and = 23,000
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. (3) to obtain the value of p. That is
For the second option, the cost for p = 83000 (3 23000)− ×
1 tie is Tshs p and the cost for 3 83000 69000−
=
shirts is Tshs 3.r 14000

Therefore, the price of each tie is
Therefore, the total cost for 1 tie 14,000 Tanzanian shillings and
Mathematics Form One From this information, form a Tanzanian shillings.
and 3 shirts is p + 3r.
the price of each shirt is 23,000

system of linear simultaneous
equations as follows:
83000 (2p + −
2 ) 9000r =


3 ) 0r =
83000 ( p + −

100

25/09/2025 15:01:17
Mathematics form 1.indd 100 25/09/2025 15:01:17
Mathematics form 1.indd 100