Answer:
x = 7
y = 3
z (max) = 4950/3 = 1650
Step-by-step explanation:
Let call
x numbers of church goup and
y numbers of Union Local
Then
First contraint
2*x + 2*y ≤ 20
Second one
1*x + 3*y ≤ 16
Objective Function
z = 150*x + 200*y
Then the system is
z = 150*x + 200*y To maximize
Subject to:
2*x + 2*y ≤ 20
1*x + 3*y ≤ 16
x ≥ 0 y ≥ 0
We will solve by using the Simplex method
z - 150 *x - 200*y = 0
2*x + 2*y + s₁ = 20
1*x + 3*y + 0s₁ + s₂ = 16
First Table
z x y s₁ s₂ Cte
1 -150 -200 0 0 = 0
0 2 2 1 0 = 20
0 1 3 0 1 = 16
First iteration:
Column pivot ( y column ) row pivot (third row) pivot 3
Second table
z x y s₁ s₂ Cte
1 -250/3 0 0 200/3 = 3200/3
0 - 4/3 0 -1 2/3 = -20/3
0 1/3 1 0 1/3 = -20/3
Second iteration:
Column pivot ( x column ) row pivot (second row) pivot -4/3
Third table
z x y s₁ s₂ Cte
1 0 0 750/12 700/6 = 4950/3
0 1 0 3/4 -1/2 = 7
0 0 1 -1/4 1/2 = 9/3
<span /><span>TLDR: Equation is 5(10 + x) = 6x. x = 50, so Sheila deposited $50 each 6 trips. Sherri deposited $60 each 5 trips. Both of them deposited $300 in total.
</span>Sherri deposited $10 more into her bank account than Sheila each 5 times. Expression: 5(x + 10).
Sheila deposited money 6 times
Expression: (6)(x) or 6x
Put it all together and the equation is 5(x+10)=6x.
Solve by distributing the 5 on the right side of the equation 5(x+10) to get 5x + 50 = 6x. Subtract 5x on both sides of equation. 5x - 5x + 50 = 6x - 5x to get 50 = 1x. Divide by 1 on each side to isolate the variable. x = 50. Sheila paid $50 in each of her 6 deposits, so she deposited $300 in total. Check the equation by replacing x with 50.
Sherri paid $60 in each of her 5 deposits because 50 + 10 is 60. 60 by 5 is also $300.
You would just do 4 x 7, which means there are 28 combinations.
(3 * 15) / 4 = 45/4 = 11....remainder 1....each grandkid gets 11 cards...equaling 44 cards....leaving 1 left for Mr. Dawson
Answer:
There are many.
Step-by-step explanation:
When you say proportional, you are looking for a ratio that is equivalent to the ratio given. In your case, there are many so you might need to be more specific. But still, we can help you figure it out.
An easy way to do this would be to scale it down to its simplest form and then move upwards. To find proportional ratios, just multiply denominator and the denominator with the same factor.
That is your ratio in its simplest form. Now we can scale up, I'll show you how to do one completely:
That's the same ratio scaled up by a factor of 2.
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That's the ratio given
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Scaled up by a factor of 4
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Scaled up by a factor of 5.
The list goes on and on.
