Two women went to a retail shop a and bought some items for their shops. akua bought 3 dozens of milk and 29 tins of milo while mansa bought 2 dozens and 31 tins of milo. how much does a tin of milo and a tin of milk cost if each of them paid 147
To find out the cost of a tin of Milo and a tin of milk, we need to set up a system of equations using the given information.
Let's assume the cost of a tin of Milo is 'x' and the cost of a tin of milk is 'y'.
According to the information given, Akua bought 3 dozens of milk (which is 3 * 12 = 36 tins) and 29 tins of Milo. She paid a total of 147, so we can write the equation as:
36y + 29x = 147 ... (Equation 1)
Similarly, Mansa bought 2 dozens of milk (which is 2 * 12 = 24 tins) and 31 tins of Milo. She also paid a total of 147, so we can write the equation as:
24y + 31x = 147 ... (Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) with two unknowns (x and y). To solve this system, we can use any method such as substitution, elimination, or matrices.
Let's solve this system of equations using the elimination method:
Multiplying Equation 1 by 24 and Equation 2 by 36 to eliminate the 'x' variable, we get:
864y + 696x = 3528 ... (Equation 3)
864y + 1116x = 5292 ... (Equation 4)
Now, subtracting Equation 3 from Equation 4, we eliminate the 'y' variable:
1116x - 696x = 5292 - 3528
420x = 1764
Dividing both sides of the equation by 420, we find:
x = 1764 / 420 = 4.2
So, the cost of a tin of Milo is 4.2.
Now, we can substitute the value of x into Equation 1 (or Equation 2) to find the cost of a tin of milk:
36y + 29 * 4.2 = 147
36y + 121.8 = 147
36y = 147 - 121.8
36y = 25.2
y = 25.2 / 36
y ≈ 0.7
So, the cost of a tin of milk is approximately 0.7.
Therefore, a tin of Milo costs 4.2 and a tin of milk costs 0.7.