Math Group
Question:
seshini
Student
Two friends go to the cinema and buy two tickets, two regular boxes of popcorn, two slush puppies and a packet of whispers.
They decide to equally split the total cost, resulting in each friend paying $56.00. If a movie ticket costs $10.00 more than a box of popcorn, which in turn costs $3.00 more than a slush puppie, which in turn costs $4.00 more than a packet of whispers. Determine the cost of a movie ticket, a box of popcorn, a slush puppie and a packet of whispers.
Answers:
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kjcdb8er Teacher
eNotes Editor
Posted by kjcdb8er on Thursday October 1, 2009 at 1:09 PMThe friends together spend 56*2 = 112 on two tickets (t), two popcorns (p), two slushes (s), and one whispers (w). So,
2t + 2p + 2s + w = 112 Also, we have:
t - p = 10
p - s = 3
s - w = 4
You can solve this by isolating variables and plugging in. But we can also solve this by putting it in matrix form and transforming it to row echelon form:
2t + 2p + 2s + 1w = 112
1t - 1p + 0s + 0w = 10
0t + 1p - 1s + 0w = 3
0t + 0p + 1s - 1w = 4 or,
[ 2 2 2 1 | 112 [ 1 0 0 0 | 25
1 -1 0 0 | 10 --> 0 1 0 0 | 15
0 1 -1 0 | 3 0 0 1 0 | 12
0 0 1 -1 | 4] 0 0 0 1 | 8 ]
So t = 25, p = 15, s = 12, and w = 8
You can check the answer to see how this checks out.
For a review on how to reduce a matrix to echelon form, you do the following:
Step 1: divide row 1 so that leading number is 1
Step 2: multiply and add so that the column of the leading number is zero in all other rows.
Step 3: repeat for each row.
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