- A large tray of sardines cost €33.5
- A 3 kg bag of squid cost €16.5
- A 2kg box of mussels cost €9.5
Explanation:
From this problem, we know that during the weekend Fiona bought some frozen seafood at the market. She bought the following things:
- A large tray of sardines
- A 3 kg bag of squid
- A 2kg box of mussels
Let:
x: The large tray of sardines
y: The 3 kg bag of squid
z: The 2kg box of mussels
Then, we have the following information:
The sardines and the squid cost €50:
[tex]x+y=50 \ ... \ eq1[/tex]
The sardines and the mussels cost €43:
[tex]x+z=43 \ ... \ eq2[/tex]
The squid and the mussels cost €26:
[tex]y+z=26 \ ... \ eq3[/tex]
Isolating x from eq 1 and substituting into eq 2:
[tex]From \ eq1: \\ \\ x=50-y \\ \\ \\ Substituting \ into \ eq2: \\ \\ (50-y)+z=43 \\ \\ -y+z=43-50 \\ \\ -y+z=-7 \ ... \ eq4[/tex]
Adding eq3 and eq4:
[tex]\ \ y+z=26 \\ \\ -y+z=-7 \\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ \\ 2z=19 \\ \\ z=9.5[/tex]
From eq 3:
[tex]y+z=26 \\ \\ y+9.5=26 \\ \\ y=26-9.5 \\ \\ y=16.5[/tex]
From eq 1:
[tex]x=50-y \\ \\ x=50-16.5 \\ \\ x=33.5[/tex]
Finally:
- A large tray of sardines cost €33.5
- A 3 kg bag of squid cost €16.5
- A 2kg box of mussels cost €9.5
Learn more:
Solving systems of linear equations: https://brainly.com/question/13799715
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