SOLUTION: A family buys 3 buckets of popcorn and 2 drinks and the total cost was $30 then a second family buys 2 buckets of popcorn and 6 drinks and their total was $34 solve this equation a
Question 1118271: A family buys 3 buckets of popcorn and 2 drinks and the total cost was $30 then a second family buys 2 buckets of popcorn and 6 drinks and their total was $34 solve this equation and find the total cost of popcorn and drinks. Found 2 solutions by Boreal, greenestamps:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! P=popcorn and D=drinks
3P+2D=30
2P+6D=34
multiply the top by -3
-9P-6D=-90
2P+6D=34
-7P=-56
P=$8 for popcorn, so 2D must equal 6 and D=$3
This checks in the second equation
popcorn is $8 each and drinks are $3 each.
Here is a common sense solution that uses EXACLTY the same arithmetic as the formal algebraic solution shown by the other tutor. Understanding the common sense solution will make it easier to understand the formal solution.
(1) Multiply the purchase by the first family by 3, so that they are buying 9 buckets of popcorn and 6 drinks for $90.
(2) The numbers of drinks in the two purchases are now the same, so the difference in price ($90-$34 = $56) is due to the difference in the number of buckets of popcorn (9-2 = 7).
(3) So the cost of each bucket of popcorn must be $56/7 = $8.
(4) Then use that cost of each bucket of popcorn with either of the purchases to determine the cost of each drink:
