At a pet store, each frog is priced at `$1` and each salamander is priced at `$8`. Jeff puchased 14 amphibians at the store for a total price of `$42`. How many frogs did Jeff purchase?

Answer

To solve the problem step by step, we can set up a system of equations based on the information given.

### Step 1: Define Variables
Let:
- \( X \) = number of frogs purchased
- \( Y \) = number of salamanders purchased

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of amphibians purchased is 14:
\[ X + Y = 14 \quad \text{(Equation 1)} \]

2. The total cost of the amphibians is $42:
\[ 1X + 8Y = 42 \quad \text{(Equation 2)} \]

### Step 3: Solve the System of Equations
We will use substitution or elimination to solve these equations. Let's use substitution.

From Equation 1, we can express \( Y \) in terms of \( X \):
\[ Y = 14 - X \quad \text{(Substituting into Equation 2)} \]

Now substitute \( Y \) into Equation 2:
\[ X + 8(14 - X) = 42 \]

### Step 4: Simplify and Solve for \( X \)
Distributing the 8:
\[ X + 112 - 8X = 42 \]

Combine like terms:
\[ -7X + 112 = 42 \]

Subtract 112 from both sides:
\[ -7X = 42 - 112 \]
\[ -7X = -70 \]

Now, divide by -7:
\[ X = 10 \]

### Step 5: Find \( Y \)
Now that we have \( X \), we can find \( Y \):
\[ Y = 14 - X = 14 - 10 = 4 \]

### Conclusion
Jeff purchased 10 frogs.