Question

Challenge You want to stock your aquarium with three types of fish: angelfish, swordtails, and tetras. Each angelfish costs \(5, each swordtail costs \)2, and each tetra costs $3. You plan to buy 20 fish.

a. Let a be the number of angelfish and s be the number of swordtails you buy. In terms of a and s, how many tetras do you buy?

b. Write and simplify an expression in terms of a and s for the total cost of your fish.

c. Of the 20 fish you buy, 4 are angelfish and 10 are swordtails. Use your expression from part (b) to find your total cost.

Short answer

(a) The number of tetras is $20-a-s$.

(b) The expression for the total cost of fish is $\$(2a-s+60)$.

(c) The total cost is localid="1648057408950" $\$\text{62}$

Step-by-step solution

(a)Step 1   Apply the concept of terms and like terms

In an algebraic expression, terms are separated by plus or minus signs.

The term coefficient refers to the number in front of the variable in any term of the expression.

A constantterm is the number which have no variable associated with it.

Like terms are the terms which have identical variable parts with same exponent on it. Constants are considered to be like terms as well.

Distributive property: $a\left(b+c\right)=a·b+a·c$

  Given information and formula used

Total number of fish is$20$

  Calculation

Let$x$be the number of tetras. So,

$\begin{array}{l}a+s+x=20\\ \Rightarrow x=20-a-s\end{array}$

(b)Step 1   Apply the concept of terms and like terms

In an algebraic expression, terms are separated by plus or minus signs.

The term coefficient refers to the number in front of the variable in any term of the expression.

A constantterm is the number which have no variable associated with it.

Like terms are the terms which have identical variable parts with same exponent on it. Constants are considered to be like terms as well.

Distributive property: $a\left(b+c\right)=a·b+a·c$

  Given information and formula used

The cost of each angel fish, swordtail and tetra is respectively $\$\text{5,}\$\text{2}$and$\$\text{3}$.

Number of angelfish is $a$, number of swordtail is $s$ and as found in part (a), number of tertras is $(20-a-s)$

  Calculation

So, the total cost of fish

$\begin{array}{l}=\$(5a+2a+3(20-a-s\left)\right)\\ =\$(5a+2s+60-3a-3s)\\ =\$(2a-s+60)\end{array}$

(c)Step 1   Apply the concept of terms and like terms

In an algebraic expression, terms are separated by plus or minus signs.

The term coefficient refers to the number in front of the variable in any term of the expression.

A constantterm is the number which have no variable associated with it.

Like terms are the terms which have identical variable parts with same exponent on it. Constants are considered to be like terms as well.

Distributive property: $a\left(b+c\right)=a·b+a·c$

  Given information and formula used

$a=4,s=10$ .

As found in part (b), the total cost for $\text{20}$fish $=\$(2a-s+60)$

  Calculation

As found in part (b), the total cost for $\text{20}$fish $=\$(2a-s+60)$

Then for $a=4$and $s=10$, the total cost is

$\begin{array}{l}=\$\left(2\right(4)-10+60)\\ =\$(8-10+60)=\$62\end{array}$