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Answer :
Weight of each large box is 18.75 kilogram and weight of each small box is 15.75 kilogram.
We have given
A delivery of 3 large boxes and 5 small boxes has a total weight of 135 kilograms.
A delivery of 9 large boxes and 7 small boxes has a total weight of 279 kilograms.
Let the large box be x and the small box be y.
Then
3x + 5y = 135....(1)
9x+ 7y = 279....(2)
Multiply equation (1) by 3, we get
9x + 15y = 405
9x+ 7y = 279
Subtract these equations , we get
8y = 126
y = 15.75
Substitute y = 15.75 in the other equation 3x + 5y = 135.
3x + 5(15.75) = 135
3x + 78.75 = 135
3x = 56.25
x = 18.75
Therefore, weight of each large box is 18.75 kilogram and weight of each small box is 15.75 kilogram.
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Rewritten by : Barada
A delivery of 3 large boxes and 5 small boxes has a total weight of 135 kilograms.
3l + 5s = 135
A delivery of 9 large boxes and 7 small boxes has a total weight of 279 kilograms
9l + 7s = 279
Another of the same type of thing, two variables, two equations, enough info to suss out the details. In this type of problem check the total against one of the factors to see if there's an even division, that's usually the avenue that leaves the prettiest whole numbers. Here you could solve the first one for s, ending up with 135/5 and 3/5
3l + 5s = 135
5s = 135-3l
s=135/5-3/5l
s=27-0.6l
Sub that s into the other equation:
9l + 7s = 279
9l + 7(27-0.6l) = 279
9l + 189-4.2l = 279
4.8l+189=279
4.8l = 90
l = 18.75
Toss that into one of the equations and solve for exact s:
9l + 7s = 279
9(18.75) + 7s = 279
s=15.75
Hope it helps to learn it, you have many avenues to approach it, solving either equation for either variable to begin with. If your numbers get ugly or you're getting frustrated sometimes helps to start over, maybe start with the other equation or a different variable, maybe you'll come across the method they designed the problem with that gives "pretty" numbers, but if you keep going even with irrational numbers like 8.6666666666666666666666, you'll get the right answer no matter which place you start.
3l + 5s = 135
A delivery of 9 large boxes and 7 small boxes has a total weight of 279 kilograms
9l + 7s = 279
Another of the same type of thing, two variables, two equations, enough info to suss out the details. In this type of problem check the total against one of the factors to see if there's an even division, that's usually the avenue that leaves the prettiest whole numbers. Here you could solve the first one for s, ending up with 135/5 and 3/5
3l + 5s = 135
5s = 135-3l
s=135/5-3/5l
s=27-0.6l
Sub that s into the other equation:
9l + 7s = 279
9l + 7(27-0.6l) = 279
9l + 189-4.2l = 279
4.8l+189=279
4.8l = 90
l = 18.75
Toss that into one of the equations and solve for exact s:
9l + 7s = 279
9(18.75) + 7s = 279
s=15.75
Hope it helps to learn it, you have many avenues to approach it, solving either equation for either variable to begin with. If your numbers get ugly or you're getting frustrated sometimes helps to start over, maybe start with the other equation or a different variable, maybe you'll come across the method they designed the problem with that gives "pretty" numbers, but if you keep going even with irrational numbers like 8.6666666666666666666666, you'll get the right answer no matter which place you start.
