From the given statement form the equations3 tomatoes and 6 mushrooms will cost 14 dollars

1. Break Down the Problem

We need to create equations based on the statement provided. We'll let:

• $T$ = cost of one tomato
• $M$ = cost of one mushroom

The statement indicates that 3 tomatoes and 6 mushrooms together cost 14 dollars. This translates to the following equation:

$3T + 6M = 14$

2. Relevant Concepts

This is a linear equation in two variables. To solve for either variable, we need an additional equation or we can express one variable in terms of the other.

3. Analysis and Detail

We can rearrange the equation to express $T$ in terms of $M$:

$3T = 14 - 6M$ $T = \frac{14 - 6M}{3}$

Alternatively, we can express $M$ in terms of $T$:

$6M = 14 - 3T$ $M = \frac{14 - 3T}{6}$

At this stage, we have two equations depending on which variable we choose to express.

4. Verify and Summarize

Without additional information, such as the individual price of either tomatoes or mushrooms, we can't derive specific numerical values for $T$ or $M$. We have successfully created an equation that represents the relationship between the cost of tomatoes and mushrooms.

Final Answer

The equation representing the cost of 3 tomatoes and 6 mushrooms is given by:

$3T + 6M = 14$