the mass of 3 dictionaries and 2 textbook is 8 kg and the mass of 3 dictionaries and 3 textbook is 9 kg. find the mass of 5 textbooks?
3d + 3t = 9
3d + 2t = 8
Subtract second equation from first, then multiply by 5.
We do like this3+3 3+2 9-8 1multiply by 5
We do like this3+3 3+2 9-8 1multiply by 5
To find the mass of 5 textbooks, we are given two equations:
Equation 1: 3d + 2t = 8, where d represents the mass of one dictionary and t represents the mass of one textbook.
Equation 2: 3d + 3t = 9.
To solve these equations, we need to eliminate one of the variables by manipulating the equations. Let's start by multiplying Equation 1 by 3 and multiplying Equation 2 by 2 to make the coefficients of 'd' in both equations equal:
3 * (3d + 2t) = 3 * 8
2 * (3d + 3t) = 2 * 9
This simplifies the equations to:
9d + 6t = 24
6d + 6t = 18
Now, let's subtract the second equation from the first equation:
(9d + 6t) - (6d + 6t) = 24 - 18
9d - 6d + 6t - 6t = 6
3d = 6
By dividing both sides of the equation by 3, we find:
d = 2
Now that we know the mass of one dictionary is 2 kg, we can substitute this value into either of the original equations to find the mass of one textbook.
Using Equation 1:
3(2) + 2t = 8
6 + 2t = 8
2t = 8 - 6
2t = 2
t = 1
Therefore, the mass of one textbook is 1 kg.
Now we can find the mass of 5 textbooks by multiplying the mass of one textbook (1 kg) by 5:
5 * 1 = 5
Therefore, the mass of 5 textbooks is 5 kg.