Marcus needs to measure out 23 liters of a solution. He is using a container that holds 16 liters. How many groups of 16 are in 23? How many times will Marcus need to fill the container? There are ___ groups of 1/6 in 2/3

Marcus will need to fill the container times

S = ax
It is required to find the value of a which make:
0 ≤ s ≤ 1 when 0 ≤ x ≤ 15
∴ s = 0 when x = 0     ⇒⇒⇒ a = 0 (unacceptable)
or s = 1 when x = 15  ⇒⇒⇒ a = s/x = 1/15

Similarly, t = by
It is required to find the value of b which make:
0 ≤ t ≤ 1 when 0 ≤ y ≤ 60
∴ t = 0 when y = 0     ⇒⇒⇒ b = 0 (unacceptable)
or t = 1 when y = 60  ⇒⇒⇒ b = t/y = 1/60



∴ x = 15s  and  y = 60t



Note: it is not matrix it is determinant