At a restaurant, four people order fried crab claws and four people order a cup of gumbo, with a total bill of $32. If only two

Question

3 years ago

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At a restaurant, four people order fried crab claws and four people order a cup of gumbo, with a total bill of $32. If only two

people had ordered the crab claws and one person ordered the gumbo, the bill would have been $12.5. How much are each order of fried crab claws and each cup of gumbo?

Mathematics

1 answer:

shusha [124] · Answer 1 · 2022-08-04T12:02:02+03:00

The cost of each order of fried crab claw is $4.5 and cost of each cup of gumbo is $3.5

Step-by-step explanation:

Let,

Cost of each fried crab claw = x

Cost of each gumbo = y

According to given statement;

4x+4y=32 Eqn 1

2x+y = 12.5 Eqn 2

Multiplying Eqn 2 by 2

$2(2x+y = 12.5)\\4x+2y=25\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 1

$(4x+4y)-(4x+2y)=32-25\\4x+4y-4x-2y=7\\2y=7$

Dividing both sides by 2

$\frac{2y}{2}=\frac{7}{2}\\y=3.5$

Putting y=3.5 in Eqn 2

$2x+3.5=12.5\\2x=12.5-3.5\\2x=9$

Dividing both sides by 2

$\frac{2x}{2}=\frac{9}{2}\\ x=4.5$

The cost of each order of fried crab claw is $4.5 and cost of each cup of gumbo is $3.5

Keywords: linear equation, subtraction

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