3 waters, 1 juice.
2 waters, 2 juices.
2 waters, 1 popcorn.
2 waters, 1 trail mix.
1 water, 2 juices.
1 water, 1 popcorn.
1 water, 1 trail mix.
2 juices, 1 trail mix.
4 = x - 1
Add 1 to both sides:
5 = x
x = 5.
Distribute the 4 first:
4y^2 + 12 y + 4 + y^2 + 3y
Collect "like" terms:
5y^2 + 15 y + 4.
This is some interesting homework...I have never done front-end estimation before...had to search it up!
2 = x - 3
Add 3 to both sides:
1.5 + 1.5 = 3.
Suppose we had 1.54 + 1.53. Our front-end estimation would be 1.5 + 1.5 = 3.
2.5 - 1.5 = 1.
Suppose we had 2.52 - 1.53. Our front-end estimation would be 2.5 - 1.5 = 1.
Foil: First, Outside, Inside, Last
First: x*x = x^2.
Outside: x*-1 = -x.
Inside: 10*x = 10x.
Last: 10*-1 = -10.
Add all the terms: x^2 - x + 10x - 10.
Combine "like" terms: x^2 + 9x - 10.
8.69 --> 8.6
3.78 --> 3.7
6.32 --> 6.3
8.6 + 3.7 + 6.3 = $18.60 [Front-end estimation].
Exact cost: 8.69+3.78+6.32 = $18.79.
Our estimate is -$0.19 lower.
Note:
1) 4 - 3.57 = 0.43
2) 7 - 7.3 = -0.3
3) 5 - 5.14 = -0.14
0.43 - 0.3 - 0.14 = -0.01
We basically estimated and ended up being 0.01 short...the exact answer is 16.01.
