There are 2 packets of flour, Y & Z.The ratio of the mass of Y to Z is 4:1. If 26g is added to Z,the ratio of the mass of Y to Z is 7:5. Find the mass of the 2 packets at first.
Y/Z= 4.0 so Y = 4 Z
Y/(26 + Z)= 1.4
Solve for Y and Z
4Z/(26 + Z) = 1.4
4Z = 36.4 + 1.4Z
2.6 Z = 36.4
Z = 14
Y = 4Z = 56
could you please show a non-algebraic way to solve this question?
sorry i need a model method to solve
Try a graphical method. Assume different values for Z. Make that the x axis.
On the y axis, plot the mass ratio 4Z/(26 + Z)
When the y value reaches 1.4, you have the correct value of Z. You also know that Y is four times Z.
To solve this problem, we can set up a system of linear equations based on the given information.
Let's assume the mass of packet Y is represented by the variable 'y' and the mass of packet Z is represented by the variable 'z'.
Based on the given information, we have the following equations:
Equation 1: The ratio of the mass of Y to Z is 4:1
This can be expressed as: y/z = 4/1
Equation 2: If 26g is added to Z, the ratio of the mass of Y to Z is 7:5
This can be expressed as: y/(z+26) = 7/5
Now, let's solve this system of equations:
Multiplying Equation 1 by 5, we get: 5y/z = 20/1
Multiplying Equation 2 by 1, we get: 1y/(z+26) = 7/5
Now, we can simplify the equations:
Equation 3: 5y = 20z
Equation 4: y = (7/5)(z+26)
We can substitute Equation 3 into Equation 4:
5(7/5)(z+26) = 20z
Simplifying further, we get: 7(z+26) = 4z
Expanding the brackets, we get: 7z + 182 = 4z
Rearranging the equation, we get: 7z - 4z = -182
Simplifying, we get: 3z = -182
Dividing both sides by 3, we get: z = -182/3
The mass of packet Z is -182/3 grams. However, negative mass doesn't make sense in this context, so let's disregard this solution.
Therefore, there is no valid solution to this problem based on the given information.