at the local per store, zebra fish cost $2.10 each and neon tetras cost $1.80 each. if marsha bought 13 fish for a total of $25.80, not including tax, how many of each type of fish did she buy?
a)7 zebra, 6 neon
b)8 zebra, 5 neon
c)6 zebra, 7 neon
d)5 zebra, 8 neon
X Zebra fish.
Y Neon fish.
Eq1: X + Y = 13.
Eq2: 2.1X + 1.8y = 25.80
Multiply Eq1 by -2.1:
-2.1x - 2.1y = -27.3
2.1x + 1.8y = 25.8
Add the Eqs:
-0.3y = -1.5
Y = -1.5 / -0.3 = 5 = Neon.
X + 5 = 13
X = 8 Zebras.
To solve this problem, let's assign variables and set up an equation.
Let's say the number of zebra fish bought by Marsha is Z, and the number of neon tetras is N.
According to the information given, the price of each zebra fish is $2.10, and the price of each neon tetra is $1.80.
The equation we can set up is:
2.10Z + 1.80N = 25.80
Now let's test the answer choices to see which satisfies the equation:
a) 7 zebra, 6 neon
Using this option, we plug in Z = 7 and N = 6 into the equation:
2.10(7) + 1.80(6) = 14.70 + 10.80 = 25.50
This option does not satisfy the equation.
b) 8 zebra, 5 neon
Using this option, we plug in Z = 8 and N = 5 into the equation:
2.10(8) + 1.80(5) = 16.80 + 9.00 = 25.80
This option satisfies the equation.
c) 6 zebra, 7 neon
Using this option, we plug in Z = 6 and N = 7 into the equation:
2.10(6) + 1.80(7) = 12.60 + 12.60 = 25.20
This option does not satisfy the equation.
d) 5 zebra, 8 neon
Using this option, we plug in Z = 5 and N = 8 into the equation:
2.10(5) + 1.80(8) = 10.50 + 14.40 = 24.90
This option does not satisfy the equation.
Therefore, the correct answer is:
b) 8 zebra, 5 neon
Marsha bought 8 zebra fish and 5 neon tetras.
To solve this problem, we can create two equations based on the given information.
Let's assume the number of zebra fish bought by Marsha is represented by 'x' and the number of neon tetras is represented by 'y'.
According to the given information, the cost of each zebra fish is $2.10, and the cost of each neon tetra is $1.80.
Equation 1: x + y = 13 - This equation represents the total number of fish bought.
Equation 2: 2.10x + 1.80y = 25.80 - This equation represents the total cost of the fish.
Now, we can solve these two equations simultaneously to find the values of x and y.
Using the substitution method:
From Equation 1, we can express x as 13 - y.
Substituting the value of x in Equation 2, we get:
2.10(13 - y) + 1.80y = 25.80
27.30 - 2.10y + 1.80y = 25.80
27.30 - 0.30y = 25.80
-0.30y = 25.80 - 27.30
-0.30y = -1.50
Dividing both sides by -0.30, we find:
y = -1.50 / -0.30
y = 5
Substituting the value of y back into Equation 1, we have:
x + 5 = 13
x = 13 - 5
x = 8
Therefore, Marsha bought 8 zebra fish and 5 neon tetras.
The answer is option b) 8 zebra, 5 neon.