Your family goes to a restaurant for dinner. there are 7 people in your family. some order the chiken dinner for $ 12 dollars and some order the steak dinner for $ 17 dollars. if the bill was $ 109 dollars, how many people ordered each dinner?

The number of people who ordered steak dinner is 5

The number of people who ordered chicken dinner is 2

Step-by-step explanation:

Given as :

The total number of people went for the dinner = 7

The total bill price for the dinner = $ 109

The price for the chicken dinner = $ 12

The price for the steak dinner = $ 17

Let The number of people who ordered chicken dinner = c

And The number of people who ordered steak dinner = s

Now, According to question

The total number of people went for the dinner = The number of people who ordered chicken dinner + The number of people who ordered steak dinner

Or, c + s = 7

And The total bill price for the dinner = The price for the chicken dinner × The number of people who ordered chicken dinner + The price for the steak dinner ×  The number of people who ordered steak dinner

Or, $ 12 × c + $ 17  × s = $ 109

Now, solving the equations

$ 12 × ( c + s ) = $ 12 × 7

Or,  $ 12 × c + $ 12  × s = $ 84

Or, (  $ 12 × c + $ 17  × s ) - (  $ 12 × c + $ 12  × s ) = $ 109 - $ 84

Or , (  $ 12 × c - $ 12  × c ) +  (  $ 17 × s - $ 12  × s ) = $ 25

Or, ( 0 ) + ( $ 5 s ) = $ 25

∴ s =

I.e s = 5

So, The number of people who ordered steak dinner = s = 5

Put the value og s in Eq A

∵,  c + s = 7

or,  c = 7 - s

Or, c = 7 - 5

I.e   c = 2

So , The number of people who ordered chicken dinner = c = 2

Hence The number of people who ordered steak dinner is 5

And The number of people who ordered chicken dinner is 2   Answer

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