SOLUTION: Your family goes to a southern-style restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14 and some order the steak dinner for $17. If the

Algebra ->  Expressions-with-variables -> SOLUTION: Your family goes to a southern-style restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14 and some order the steak dinner for $17. If the      Log On


   

Question 1131381: Your family goes to a southern-style restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14 and some order the steak dinner for $17. If the total bill was $99, how many people ordered each dinner?
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = number that ordered chicken dinner
+6+-+x+ = number that ordered steak dinner
--------------------------------------------------------
+14x+%2B+17%2A%28+6+-+x+%29+=+99+
+14x+%2B+102+-+17x+=+99+
+3x+=+3+
+x+=+1+
and
+6+-+x+=+5+
---------------------
1 ordered chicken dinner
5 ordered steak dinner
--------------------------------
check:
+14%2A1+%2B+17%2A5+=+99+
+14+%2B+85+=+99+
+99+=+99+
OK

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


A solution using formal algebra is of course valid; and it may be a requirement.

But if you only need to solve the problem by any method you want, use a little mental arithmetic and some logical reasoning.

If all 6 people had ordered the steak dinner, the total cost would have been $17*6 = $102; the actual total cost was $99, which is $3 less. Since a chicken dinner costs $3 less than a steak dinner, there must have been just one person who ordered chicken.

ANSWER: 1 chicken and 5 steak