Question

Anna bought 8 goldfish and 2 rainbow fish for her aquarium. The rainbow fish cost 6 dollars more than the goldfish. She paid a total of 37 dollars for the fish. Write an equation to find the cost of each of the goldfish.

Answer 1

Let the price of the goldfish be x
Let the price of the rainbow fish be y

Anna bought 8 fish, therefore, Anna paid 8x for the gold fish
Anna bought 2 rainbow fish, therefore, Anna paid 2y for the rainbow fish

We know that the total amount that Anna paid is 37$.
Therefore:
8x + 2y = 37 ..................> equation I

Now, we know that the rainbow fish cost 6$ more than the goldfish (since the verb "cost" is plural, therefore the total payment of rainbow fish is 6$ more than the total payment of gold fish).
Based on this,
2y + 6 = 8x 
2y = 8x - 6 ...................> equation II

Substitute by equation II in equation I, we can get the following equation:
8x + 8x - 6 = 37 
16x = 43 ................> The desired equation (equation III)

Solving equation III, we can calculate the price of one gold fish as follows:
16x = 43
x = 2.6875$

If we substitute by the value of x in equation I, we can calculate the price of one rainbow fish as follows:
8(2.6875) + 2y = 37
y = 7.75$