Answer:
1.25
Step-by-step explanation:
type in your calculator:
-1.5+2.75 OR 2.75-1.5
you should get the same answer
If you divide 537 in to 12 groups. each group would have 44 cookies and you would have 9 left.
Let x be the number of weeks; therefore, the two linear equations are
![\begin{gathered} T=2+7x \\ \text{and} \\ C=11+4x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20T%3D2%2B7x%20%5C%5C%20%5Ctext%7Band%7D%20%5C%5C%20C%3D11%2B4x%20%5Cend%7Bgathered%7D)
Where T stands for the punches on the tea punch card and C for the punches on the coffee punch card.
Solving by substitution. Set T=C, then
![\begin{gathered} T=C \\ \Rightarrow2+7x=11+4x \\ \Rightarrow3x=9 \\ \Rightarrow x=\frac{9}{3}=3 \\ \Rightarrow x=3 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20T%3DC%20%5C%5C%20%5CRightarrow2%2B7x%3D11%2B4x%20%5C%5C%20%5CRightarrow3x%3D9%20%5C%5C%20%5CRightarrow%20x%3D%5Cfrac%7B9%7D%7B3%7D%3D3%20%5C%5C%20%5CRightarrow%20x%3D3%20%5Cend%7Bgathered%7D)
Thus, substitute the value of x=3 into the first equation,
![\begin{gathered} x=3 \\ \Rightarrow T=2+7\cdot3=23 \\ \Rightarrow T=23 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D3%20%5C%5C%20%5CRightarrow%20T%3D2%2B7%5Ccdot3%3D23%20%5C%5C%20%5CRightarrow%20T%3D23%20%5Cend%7Bgathered%7D)
Thus, after 3 weeks, Josiah will have the same number of punches on each card, and he will have 23 punches on each card.
Answer:
[12, 15]
Step-by-step explanation:
{6x + 5y = 147
{8x + 4y = 156
-¾[8x + 4y = 156]
{6x + 5y = 147
{-6x - 3y = -117 ← New Equation
________________
2y = 30
___ ___
2 2
y = 15 [Plug this back into both equations to get the x-coordinate of 12]; 12 = x
So, using the Elimination Method, what I did here was took the bottom equation and multiplied it by -¾, turning 8x to -6x, canceling out all <em>x-terms</em><em>.</em><em> </em>It does not matter which variable you choose to eliminate, as long as you know what you are doing.
I am joyous to assist you anytime.
You are doing 133 divided by 6 to give you 55