Answer:
2 3/5
Step-by-step explanation:
To solve this problem, we need to pick numbers from the table then this number will be substituted into the equation. But first, we equate the numbers such as below:
4x - 2y = 8
Transpose -2y to the right side such as:
4x = 8 + 2y
4x - 8 = 2y
(4x -8)/2 = y
2x - 4 =y
From the table, let us choose x = 0
y = 2x -4
y = 2(0) -4
y = -4
From the table, let choose another value of x such as x=1
y = 2(1) -4
y = 2 - 4
y = -2
This will prove that the values in the table are correct.
Answer:
![x=0.25\,,\,y=1.75\,,\,z=0.25](https://tex.z-dn.net/?f=x%3D0.25%5C%2C%2C%5C%2Cy%3D1.75%5C%2C%2C%5C%2Cz%3D0.25)
Step-by-step explanation:
Let
denotes number of pencils, markers, erasers respectively.
For Andrea:
![6x+7y+8z=15.75\,\,\,(i)](https://tex.z-dn.net/?f=6x%2B7y%2B8z%3D15.75%5C%2C%5C%2C%5C%2C%28i%29)
For Justin:
![6x+8y+5z=16.75\,\,\,(ii)](https://tex.z-dn.net/?f=6x%2B8y%2B5z%3D16.75%5C%2C%5C%2C%5C%2C%28ii%29)
For Virginia:
![5x+5y+7z=11.75\,\,\,(iii)](https://tex.z-dn.net/?f=5x%2B5y%2B7z%3D11.75%5C%2C%5C%2C%5C%2C%28iii%29)
On subtracting equations (i) and (ii), we get
![(6x+7y+8z)-(6x+8y+5z)=15.75-16.75\\-y+3z=-1\\y-3z=1\\y=1+3z](https://tex.z-dn.net/?f=%286x%2B7y%2B8z%29-%286x%2B8y%2B5z%29%3D15.75-16.75%5C%5C-y%2B3z%3D-1%5C%5Cy-3z%3D1%5C%5Cy%3D1%2B3z)
Put
in equation (i)
![6x+7(1+3z)+8z=15.75\\6x+29z=8.75\,\,\,(iv)](https://tex.z-dn.net/?f=6x%2B7%281%2B3z%29%2B8z%3D15.75%5C%5C6x%2B29z%3D8.75%5C%2C%5C%2C%5C%2C%28iv%29)
Put
in equation (iii)
![5x+5(1+3z)+7z=11.75\\5x+22z=6.75\,\,\,(v)](https://tex.z-dn.net/?f=5x%2B5%281%2B3z%29%2B7z%3D11.75%5C%5C5x%2B22z%3D6.75%5C%2C%5C%2C%5C%2C%28v%29)
Multiply equation (iv) by 5 and equation (v) by 6 and then subtract both the equations.
![5(6x+29z)-6(5x+22z)=5(8.75)-6(6.75)\\13z=3.25\\z=\frac{3.25}{13}=0.25](https://tex.z-dn.net/?f=5%286x%2B29z%29-6%285x%2B22z%29%3D5%288.75%29-6%286.75%29%5C%5C13z%3D3.25%5C%5Cz%3D%5Cfrac%7B3.25%7D%7B13%7D%3D0.25)
Put
in equation ![y=1+3z](https://tex.z-dn.net/?f=y%3D1%2B3z)
![y=1+3(0.25)=1.75](https://tex.z-dn.net/?f=y%3D1%2B3%280.25%29%3D1.75)
Put
in equation (i)
![6x+7(1.75)+8(0.25)=15.75\\6x+12.25+2=15.75\\6x=1.5\\x=0.25](https://tex.z-dn.net/?f=6x%2B7%281.75%29%2B8%280.25%29%3D15.75%5C%5C6x%2B12.25%2B2%3D15.75%5C%5C6x%3D1.5%5C%5Cx%3D0.25)
Answer:
no se jejfjekqkznbeoqnzne
Answer:
11 cans
Step-by-step explanation:
1 hr = 60 min
33 hrs = ? min
Setup proportion and solve for x:
![\frac{1hr}{60 min} =\frac{33hrs}{xmin}](https://tex.z-dn.net/?f=%5Cfrac%7B1hr%7D%7B60%20min%7D%20%3D%5Cfrac%7B33hrs%7D%7Bxmin%7D)
Do butterfly method and get x = 1980 minutes
Then take the 1980 divide it by 180 to find the number of cans.
![\frac{1980}{180} =11](https://tex.z-dn.net/?f=%5Cfrac%7B1980%7D%7B180%7D%20%3D11)