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shtirl [24]
3 years ago
14

2. A ski lodge offers two weekend packages. Package A provides 2 nights and 3 meals for $280. Package B provides 2 nights and 5

meals for $320. Write and solve a system of equations to find the costs per night and per meal. (Assume the cost per night and cost per meal are the same for both packages.) Use n to represent the cost per night and m to represent the cost of each meal. (8 points)
Step 1: The equation representing package A is given. Complete the system of equations by writing an equation to represent package B. (1 point)

Package A: 2n + 3m = 280
Package B: ___________________



Step 2: Select a method for solving the system. Which method did you choose? Why? (2 points)




Step 3: Solve the system of equations to find the costs per night and per meal. Show your work.(3 points)













Step 4: Explain the meaning of the solutions for m and n. (2 points: 1 point each)
Mathematics
1 answer:
Degger [83]3 years ago
6 0

Answer:

1st formula 2n + 3m = 280

2nd formula 2n + 5m = 320

rearrange 1st formula to equal n:

   2n = -3m + 280

    n = -3/2 m + 140

rearrange 2nd formula to equal n:

2n = -5m + 320

n = -5/2m + 160

so now you have

-3/2m + 140 = -5/2m + 160

Rearrange to become:

-3/2m + 5/2m = 160 - 140

m = 20

Now place 20 into the very 1st equation in place of the letter m

2n + 3(20) = 280

2n + 60 = 280

2n = 220

n = 110

so it costs $110 per night, $20 per meal

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A 30 Oz box of Lucky Charms cost $4.50 a 20 oz box cost $3.60 what is the unit price of each box
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We need to find the unit price of each box.

So, a box that weighs 30 Oz costs $4.50.

lets say that 30 Oz box is named box 1. We can use unitary method to find out the unit price of box 1.

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Now,

30 Oz costs $4.50

therefore, 1 Oz should cost:

\frac{4.50}{30} =0.15 dollars

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Now, lets say the 20 Oz box is named box 2. Again we can use unitary method to find out the unit price of box 2.

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3 0
3 years ago
35=3x+14 could anyone help me fast please I also need to show work!
Neporo4naja [7]

Answer:

\boxed {\tt x=7}

Step-by-step explanation:

We are given the equation

35=3x+14

We want to solve for x, therefore we must isolate x on one side of the equation.

14 is being added to 3x. The inverse of addition is subtraction. Subtract 14 from both sides of the equation.

35-14=3x+14-14

35-14=3x

21=3x

x is being multiplied by 3. The inverse of multiplication is division. Divide both sides of the equation by 3.

\frac{21}{3} =\frac {3x}{3}

\frac{21}{3}=x

7=x

Let's check our solution. Plug 7 in for x and solve.

35=3x+14

35=3(7)+14

35=21+14

35=35

This checks out, so we know our solution, <u>x=7 </u>is correct.

8 0
4 years ago
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