Question

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 people 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.

Answer 1

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.

Setting up the equations:

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

Substitution method:

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].