Forming simultaneous equation

Question

A cutlery manufacturing company makes knivesand spoons. The cost of making 12 knives and 12

spoons is Ksh600/and the cost of making 15 knives and 9 spoons is given as Ksh630/. The 

shop makes a 25% and 45% profit on each knife and each spoon respectively. Required:Express 

the above costs of making a knife and a spoon as simultaneous equationsand hence find the cost 

of making one spoon and one knife.

Answer 1

Let "k" equal the cost to make a knife. Let "s" equal the cost of making a spoon.

Then "the cost of making 12 knives and 12 spoons is Ksh600" can be written as:

12k + 12s = 600

And "the cost of making 15 knives and 9 spoons is given as Ksh630" can be written as:

15k + 9s = 630

Now to solve:

Dividing both sides of "12k + 12s = 600" by 12 gives:

k + s = 50 meaning that k = 50 - s

Dividing both sides of "15k + 9s = 630" by 3 gives:

5k + 3s = 210. Plugging in "50 - s" in place of "k" (because k = 50 - s) we get:

5(50 - s) + 3s = 210

250 - 5s + 3s = 210

250 - 2s = 210

250 - 210 = 2s

40 = 2s

s = 20

Plugging in s = 20 into "k = 50 - s" gives:

k = 50 - 20

k = 30

So the cost to manufacture a knife is Ksh30 and the cost to manufacture a spoon is Ksh20

Notice that the profit does not play a part in answering this question.