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...

The 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.