Let the first number = x
The second number would be x +1
3rd number = x +2
4th number = x +3
5th number = x+4
6th number = x+5
7th number = x +6
8th number = x +7
9th number = x+8
The sum is 279
Combine like terms in the 9 numbers to get: 9x + 36 = 279
Solve for x:
9x + 36 = 279
Subtract 36 from both sides:
9x = 243
Divide both sides by 9:
x =27
The first number is 27
The last number would be 27 + 8 = 35
The sum of the first and last would be 27 + 35 = 63
Answer:
- large: 40 lbs
- small: 20 lbs
Step-by-step explanation:
A system of equations can be written for the weights of the boxes based on the relationships given in the problem statement. One equation will be for the total weight of 1 large and 1 small box; the other will be for the total weight of 70 large and 60 small boxes.
Let L and S represent the weights of Large and Small boxes, respectively. The system of equations is ...
L + S = 60 . . . . . . combined weight is 60 lbs
70L +60S = 4000 . . . . weight of boxes in the truck
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We can solve this by substituting for s in the second equation.
70L +60(60 -L) = 4000
10L = 400 . . . . . . . . . subtract 3600, simplify
L = 40
S = 60 -L = 20
A large box weighs 40 pounds; a small box weighs 20 pounds.
let's recall that an inverse function has the same pair of coordinates as the original function, but backwards, or namely the inverse's range is the original's domain.
