Question

A store sells yogurt in small, medium, and large sizes. A small yogurt costs $2, a medium costs $3, and a large costs $5. In one hour, the shop sold 27 yogurts for $98. There were five more large yogurts than small yogurts. The matrix below represents the system of equations in this situation.

Answer 1

Let s,m,l be the numbers of small, medium, and large yogurts. The system is

s + m + l = 27
2s + 3m + 5l = 98
-l + s = -5 (equivalently l = s + 5 → -s + 0m + l = 5)

The augmented matrix (s,m,l | RHS) is
[ 1 1 1 | 27 ]
[ 2 3 5 | 98 ]
[ -1 0 1 | 5 ]

Row-reduction (quick steps):
- R2 ← R2 − 2·R1 → [0 1 3 | 44]
- R3 ← R3 + R1 → [0 1 2 | 32]
- R2 ← R2 − R3 → [0 0 1 | 12] ⇒ l = 12
- Back-substitute: from R3: m + 2l = 32 ⇒ m = 32 − 24 = 8
- From R1: s = 27 − m − l = 27 − 8 − 12 = 7

So the shop sold 7 small, 8 medium, and 12 large yogurts.