Question

Rick bought some tetra fish and goldfish for his fish tank. He bought twice as many goldfish as he did tetras. Each goldfish costs $1.50, and each tetra fish costs $2.00. He spent $20 on the fish. Which system can be used to represent x, the number of tetra fish, and y, the number of goldfish, he purchased?

x = 2 y. 2 x + 1.5 y = 20
2 x = y. 2 x + 1.5 y = 20
x = y. 2 x + 1.5 y = 20
x + y = 20. 2 x + 1.5 y

Answer 1

B. 2x = y; 2x +1.5y = 20

Explanation:

The two given relations can be written as two equations, one for the numbers of fish, and one for their cost.

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number of fish

The number of goldfish (y) is twice the number of tetras (x), so one equation can be ...

2x = y

cost of fish

The tetras (x) are $2 each, and the goldfish (y) are $1.50 each. Their total cost is the sum of products of the number of fish and the cost of each. That total is given as $20, so the other equation could be ...

2x +1.5y = 20

Then the appropriate system of equations is ...

• 2x = y
• 2x +1.5y = 20

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Additional comment

The solution can be found by substituting for 2x to get ...

y +1.5y = 20 . . . . . . substitute for 2x

y = 20/2.5 = 8 . . . . divide by the coefficient of y

x = y/2 = 4 . . . . . . . find the number of tetras

Rick bought 4 tetras and 8 goldfish.

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The wording "twice as many goldfish as tetras" easily causes confusion. It is helpful to reword it as "goldfish were twice the number of tetras."