X + 6 = 33
x = 27
hope this helps :D
The total number of gifts = x+y.
The inequality is:
![x+y \geq 24](https://tex.z-dn.net/?f=x%2By%20%20%5Cgeq%2024)
Key chains cost $1, Magnets $0.50
Total Cost = x + 0.5y
Inequality is:
![x+0.5y \leq 20](https://tex.z-dn.net/?f=x%2B0.5y%20%20%5Cleq%2020)
Without graphing you can solve system by using substitution:
![y = 24 - x \\ \\ x + 0.5(24-x) = 20 \\ \\ 0.5x +12 = 20 \\ \\ x = 16 \\ \\ y = 24-16 = 8](https://tex.z-dn.net/?f=y%20%3D%2024%20-%20x%20%20%5C%5C%20%20%5C%5C%20x%20%2B%200.5%2824-x%29%20%3D%2020%20%20%20%5C%5C%20%20%5C%5C%200.5x%20%2B12%20%3D%2020%20%20%5C%5C%20%20%5C%5C%20x%20%3D%2016%20%5C%5C%20%20%5C%5C%20y%20%3D%2024-16%20%3D%208)
This is one solution where the maximum x value is given.
So the most keychains that can be purchased is 16. However, because magnets are cheaper, more can be purchased as long as cost remains under 20.
If you solve both inequalities for "y", you get the upper and lower bounds for how many magnets can be purchased given a quantity of keychains.
![24-x \leq y \leq 40 -2x \\ \\ x \leq 16](https://tex.z-dn.net/?f=24-x%20%20%5Cleq%20y%20%20%5Cleq%2040%20-2x%20%5C%5C%20%20%5C%5C%20x%20%5Cleq%2016)
This is complete solution which gives all possible combinations.
(Graph is Attached)
A²+B²=C²
6²+8²=C²
C²=100
C=10
Therefore the length of AB is 10 units
12 is 1 more than 11
12 is one less than 13
this ok?
Answer:
10 miles.
Step-by-step explanation:
Let x be the number of miles on Henry's longest race.
We have been given that Henry ran five races, each of which was a different positive integer number of miles.
We can set an equation for the average of races as:
![\frac{\text{The sum distances of 5 races}}{5}=4](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BThe%20sum%20distances%20of%205%20races%7D%7D%7B5%7D%3D4)
As distance covered in each race is a different positive integer, so let his first four races be 1, 2, 3, 4.
Now let us substitute the distances of 5 races as:
![\frac{1+2+3+4+x}{5}=4](https://tex.z-dn.net/?f=%5Cfrac%7B1%2B2%2B3%2B4%2Bx%7D%7B5%7D%3D4)
![\frac{10+x}{5}=4](https://tex.z-dn.net/?f=%5Cfrac%7B10%2Bx%7D%7B5%7D%3D4)
Let us multiply both sides of our equation by 5.
![\frac{10+x}{5}*5=4*5](https://tex.z-dn.net/?f=%5Cfrac%7B10%2Bx%7D%7B5%7D%2A5%3D4%2A5)
![10+x=20](https://tex.z-dn.net/?f=10%2Bx%3D20)
Let us subtract 10 from both sides of our equation.
![10-10+x=20-10](https://tex.z-dn.net/?f=10-10%2Bx%3D20-10)
![x=10](https://tex.z-dn.net/?f=x%3D10)
Therefore, the maximum possible distance of Henry's longest race is 10 miles.