Two dozen of eggs and aloaf of bread cost k17.50.Half a dozen eggs and two loaves of bread cost K14.00.Fine the cost of a dozen of eggs
2d+1b = 17.50
1/2 d + 2b = 14.00
d = 6.00
E = price dozen of eggs
B = price a loaf of bread
Translate the text into equations.
2 E + B = 17.5
E / 2 + 2 B = 14
Try to solve this sydtem.
The solution is:
E = 6 , B = 5.5
To find the cost of a dozen of eggs, we need to solve the given system of equations. Let's assign variables:
Let x represent the cost of a dozen eggs in Kwacha (K).
From the first piece of information, we can create an equation:
24x + 1 * cost of a loaf of bread = K17.50
From the second piece of information, we can create another equation:
6x + 2 * cost of a loaf of bread = K14.00
To find the cost of a dozen eggs (x), we will solve these two equations simultaneously.
First, let's eliminate the cost of a loaf of bread.
Multiplying the first equation by 2 and the second equation by 1 will make the coefficients of the loaf of bread equal:
2(24x + 1 * cost of a loaf of bread) = 2(K17.50)
1(6x + 2 * cost of a loaf of bread) = 1(K14.00)
Simplifying:
48x + 2 * cost of a loaf of bread = K35.00
6x + 2 * cost of a loaf of bread = K14.00
Now we can subtract the second equation from the first to eliminate the term "2 * cost of a loaf of bread":
(48x + 2 * cost of a loaf of bread) - (6x + 2 * cost of a loaf of bread) = (K35.00) - (K14.00)
42x = K21.00
Dividing both sides by 42:
x = K21.00 / 42
x = K0.50
Therefore, the cost of a dozen eggs (12 eggs) is K0.50.