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Allushta [10]
3 years ago
13

At a restaurant, four people ordered fried crab cakes and four people ordered a cup of gumbo, with a total of $31. If only two p

eople had ordered the crab cakes and one person ordered the gumbo, the bill would have been $12.25. How much are each order of fried crab cakes and each cup of gumbo? (Can you please show the steps?) Thank you.
Mathematics
1 answer:
ruslelena [56]3 years ago
7 0

Answer:

Fried crab cakes = $4.50

Cup of gumbo = $3.25

Step-by-step explanation:

Let's make the price of fried crab cakes = x and the price of a cup of gumbo = y. Set up two equations for x and y and solve for each variable.

<h3><u>Setting up the equations:</u></h3>

4 people ordered x and 4 people ordered y for a total of 31 dollars, so this equation would look like: 4x + 4y = 31

2 people ordered x and 1 person ordered y for a total of $12.25, so this equation would look like: 2x + y = 12.25

<h3><u>Substitution method:</u></h3>

Now you have your two equations-- solve for a variable in one of the equations and substitute that value into the other equation.

The easiest way to start would be to solve for y in the second equation by subtracting 2x from both sides.

y = 12.25 - 2x

Substitute this value into the first equation.

4x + 4(12.25 - 2x) = 31

Now solve for x-- start by distributing 4 inside the parentheses.

4x + (49 - 8x) = 31

Combine like terms.

-4x + 49 = 31

Subtract 49 from both sides.

-4x = -18

Divide both sides by -4.

x = 4.5

Substitute this value of x into our starting equation for which we solved for y.

2(4.5) + y = 12.25

Multiply 2 and 4.5 together.

9 + y = 12.25

Subtract 9 from both sides.

y = 3.25

Each order of fried crab cakes is worth the x-value [$4.50] and each cup of gumbo is worth the y-value [$3.25].

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Jon caught four fish that weighed a total of 252 pounds. The kingfish weighed twice as much as the amberjack and the white marli
Allushta [10]

Answer:

  • amberjack, 21 lbs
  • kingfish, 42 lbs
  • white marlin, 84 lbs
  • tarpon, 105 lbs

Step-by-step explanation:

Let k, a, m, t represent the weights of the kingfish, amberjack, marlin, and tarpon, respectively. The problem statement tells us ...

  • k = 2a
  • m = 2k
  • t = 5a
  • k + a + m + t = 252

Using substitution, we can rewrite the last equation as ...

... (2a) + (a) + 2(2a) + (5a) = 252

... 12a = 252 . . . . . collect terms

... a = 21 . . . . . . . . .divide by 12

Then k = 2a = 42; m = 2k = 84; t = 5a = 105.

8 0
3 years ago
I need help!!
Natasha2012 [34]

Answer:

The exact solution is

x = \frac{Ln(60)}{7*Ln(5)}

And the approximation to three decimal places is:

x = 0.363

Step-by-step explanation:

Here we have the equation:

5^{7*x} = 60\\

Now we can remember a property of the natural logarithm function:

Ln(a^n) = n*Ln(a)

Now we can apply the Ln( ) function to both sides of that equation to get:

Ln(5^{7*x}) = Ln(60)

Then we get:

7*x*Ln(5) = Ln(60)

Solving that for x we get:

x = \frac{Ln(60)}{7*Ln(5)}  = 0.363

So the exact solution is:

x = \frac{Ln(60)}{7*Ln(5)}

And the approximation to three decimal places is:

x = 0.363

7 0
3 years ago
What is 3627×673:(876)?
Delicious77 [7]
3627 x 673:(876)= 2138290596 I got that by taking 3627x876(876) and got that
7 0
3 years ago
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On a horizontal number line, numbers are what
Vikentia [17]

Answer:

to the right of zero if postive if negative left

6 0
2 years ago
Read 2 more answers
A circle's radius is 14 centimeters.
spayn [35]

Answer:

Circumference of circle = 87.92 centimeter

Step-by-step explanation:

In the given question;

Radius of circle = 14 centimeters

Value of π = 3.14

Find:

Circumference of circle

Computation:

⇒ Circumference of circle = 2πr

where r = Radius of circle

⇒ Circumference of circle = 2(3.14)(14)

⇒ Circumference of circle = (6.28)(14)

Circumference of circle = 87.92 centimeter

4 0
3 years ago
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