### Brain Teasers

# Something's Fishy

The fish market is selling several kinds of fish. But there aren't any prices listed. You ask about the prices, but all the seller will tell you is this:

1. A pound of salmon and a pound of bass are $12.

2. A pound of bass and a pound of swordfish are $10.

3. A pound of salmon and a pound of swordfish are $8.

4. A pound of swordfish and a pound of catfish are $5.

Each price per pound is a whole-dollar amount. How much is the price per pound for each kind of fish?

1. A pound of salmon and a pound of bass are $12.

2. A pound of bass and a pound of swordfish are $10.

3. A pound of salmon and a pound of swordfish are $8.

4. A pound of swordfish and a pound of catfish are $5.

Each price per pound is a whole-dollar amount. How much is the price per pound for each kind of fish?

### Hint

1. Assign letter names to the different kinds of fish and write equations to decide each combination. For example: salmon = a, bass = b, a + b = $12.2. If the salmon and the bass together cost $12, and the bass and the swordfish together cost $10, what is the price difference between the salmon and the swordfish?

### Answer

Salmon = $5 per poundBass = $7 per pound

Swordfish = $3 per pound

Catfish = $2 per pound

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## Comments

Good one!!

But I want to know where you are shopping to get $5/lb. for Salmon!!

But I want to know where you are shopping to get $5/lb. for Salmon!!

I would get ticked off at a seller who did that.

A solution explaining how to get the answers would be nice!

Simple simultaneous equations problem.

I did it quickly in my head by adding equations 1 & 2 and subtracting equation 3 from the result.

salmon + bass = 12

+ swordfish + bass = 10

= salmon + swordfish + 2bass = 22

- salmon + swordfish = 8

= 2bass = 14

bass = 7

The rest is simple from there.

salmon + bass = 12

+ swordfish + bass = 10

= salmon + swordfish + 2bass = 22

- salmon + swordfish = 8

= 2bass = 14

bass = 7

The rest is simple from there.

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