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?
math - Steve, Monday, September 19, 2016 at 5:17am
3d+2t = 8
3d+3t = 9
clearly, t=1
i cant understand it
math - Steve, Monday, September 19, 2016 at 5:42am
well, just look. They added just one textbook, and the weight grew by 1 kg. Clearly the extra textbook weighed 1 kg.
Or, algebraically,
3d+3t=9
3s+2t=8
subtract and you get rid of the d's, leaving
0d+1t = 9-8
t=1
but in question we find the mass of 5 textbooks? not fifth textbook
Oh my goodness!
Steve showed you that
1 textbook weighs 1 kg
so how much will 5 textbooks weigh ?
To find the mass of 5 textbooks, we first need to determine the mass of one textbook.
We know that the mass of 3 dictionaries and 2 textbooks is 8 kg. From this, we can set up the equation 3d + 2t = 8, where d represents the mass of one dictionary and t represents the mass of one textbook.
We also know that the mass of 3 dictionaries and 3 textbooks is 9 kg. From this, we can set up the equation 3d + 3t = 9.
By subtracting the two equations, we can eliminate the variable d.
(3d + 3t) - (3d + 2t) = 9 - 8
3t - 2t = 1
t = 1
This means that the mass of one textbook is 1 kg.
To find the mass of 5 textbooks, we simply multiply the mass of one textbook by 5.
5 textbooks * 1 kg = 5 kg
Therefore, the mass of 5 textbooks is 5 kg.