Question

help please

Addison and Caden prefer tetra fish to goldfish. Addison buys 5 neon tetras and 4 cardinal tetras for $15.50. Caden buys 6 neon tetras and 10 cardinal tetras for $26.40.

A. Write a system of equations that can be used to find n, the cost of 1 neon tetra, and c, the cost of 1 cardinal tetra.

B.What is the cost of 1 neon tetra?

Answer 1

Here, you have to set up a system of equalities that allows us to model the situation.
Let's first model what Addison bought; this being 5 neon tetras (n) and 4 cardinal tetras (c) and paid 15.5$ so therefore, a model would be: \[5n +4c=15,50\]
That will be the first equation, now for Cadens model; she bought 6 neon tetras and 10 cardinal tetra, and paid 26.40$ which means that the model for her purchse is:
\[6n +10c=26,40\]
Now, in order to find the prices for each type of fish we will then build the system of equation, and it will be a 2x2 type, since we have two variables and two equations:
\[5n+4c=15,50\]
\[6n+10c=26,40\]

Answer 2

Now you can solve that using any method you have been taught.

Answer 3

thank youuuu

Answer 4

yay @Tommynaiter

Answer 5

You need to setup 2 equations with 2 variables. You get the following: \[5n+4c=15.50\]\[6n+10c=26.40\]
Here is n neon and c is cardinal. Do you see where the equations come from?

Answer 6

yes but i have trouble finding the price

Answer 7

Alright. So do you know the method substitution?

Answer 8

yes

Answer 9

So you want to use that.

Answer 10

sure

Answer 11

So lets do it in small steps. Start by isolating n in the first equation. \[5n+4c=15.50\]\[n=?\]

Answer 12

ok

Answer 13

Do you know how to isolate n?

Answer 14

you divide

Answer 15

First we subtract 4c. \[5n+4c=15.50\]\[5n=15.50-4c\] Now we divide with 5 \[n=3.1-\frac{4}{5}c\]

Answer 16

subtract 4c

Answer 17

Yeap, it looks like you know how to solve n.

Answer 18

So the next step is to insert the value for n into the 2nd equation.

Answer 19

ok

Answer 20

We had the 2nd equation: \[6n+10c=26.40\] Insert the values for n: \[6*(3.1-\frac{4}{5}c)+10c=26.40\]

Answer 21

Do you follow what I just did?

Answer 22

yes

Answer 23

Good, so now we want to isolate c. Then we have the price for c.

Answer 24

ok

Answer 25

Can you do that?

Answer 26

you divide

Answer 27

right

Answer 28

There is a couple of steps. First I would get rid of the parentheses.

Answer 29

ok

Answer 30

\[6∗(3.1−\frac{4}{5}c)+10c=26.40\]\[6*3.1=18.6\]\[6*(-\frac{4}{5}c)=-\frac{24}{5}c\] So you get \[18.6-\frac{24}{5}c+10c=26.40\]

Answer 31

ok

Answer 32

So we continue to solve c. Subtract 18.6 \[-\frac{24}{5}c+10c=7.8\] add the c's together \[\frac{26}{5}c=7.8\] multiply with 5 \[26c=39\] divide with 26 \[c=1.5\]

Answer 33

Do you understand how I solved c?

Answer 34

yes

Answer 35

Good, so now that we know the price for cardinal. We just insert the price into either one of the equations and find a value for n. \[5n+4c=15.50\] insert \[c=1.5\] \[5n+4*1.5=15.50\]\[5n+6=15.50\] subtract 6 \[5n=9.50\] divide with 5 \[n=1.90\]

Answer 36

So the price for the cardinal (c) is 1.5 and the price for neon (n) is 1.9

Answer 37

ok thank youuuu

Answer 38

Yea, I hope you understand it :) else just ask

Answer 39

I am always willing to help, if you'd like you can follow me to see if im online :)

Answer 40

ok thanks :)

Answer 41

You're welcome, have a good day @ameliagrace417 :D

Answer 42

you tooo @Tommynaiter :)