Word problem solve by substitutiuon

[basix10]

At a fundraising BBQ the cost of a plate for a child is $5.50 and $12.00 for an adult plate. The total number of people is 546. The total bill for the food is $5115.50.

I can solve this by the Elimination Method, but we are asked to solve by the Substitution Method, and I am stumped!

So far I have;

a+c=546
12a+5.5c=511.5
What do I do next?

Thank you

 

[Deleted member 4993]

At a fundraising BBQ the cost of a plate for a child is $5.50 and $12.00 for an adult plate. The total number of people is 546. The total bill for the food is $5115.50.

I can solve this by the Elimination Method, but we are asked to solve by the Substitution Method, and I am stumped!

So far I have;
First define your variables:

a = # of adult plates sold

c = # of child plates sold

a+c=546............................................................(1)

12a+5.5c=511.5............................................................(2)

from (1)

a = 546 - c ............................................................(3)

Substituting for a in (2)

12(546 - c) + 5.5c = 511.5

solve for 'c' from above - then solve for 'a' using (3)

What do I do next?

Thank you

 

[basix10]

There was a bit of a problem with the 5115.5.. Typo error!

12(546 - c) + 5.5c = 5115.5

If c=221 then appling that to 3:

a = 546 - 221 = 325

The answer would be;

a=325, c=221

Check:

a+b=546
325+221=546 True

12a+5.5b=5115.5
325(12)+221(5.5)=5115.5 True

GREAT!

Thank you sooo much.. It is sincerely apprciated