Alright, let's go through this problem step-by-step to understand the relationship between the total cost [tex]\( t \)[/tex], the number of peaches [tex]\( p \)[/tex], and the cost per peach [tex]\( d \)[/tex].
1. Understanding the Variables:
- [tex]\( t \)[/tex] represents the total amount of money Mary spends.
- [tex]\( p \)[/tex] represents the number of peaches Mary buys.
- [tex]\( d \)[/tex] represents the cost of one peach in dollars.
2. Formulating the Equation:
- The total cost [tex]\( t \)[/tex] is the amount of money Mary spends on buying [tex]\( p \)[/tex] peaches.
- The cost per peach is [tex]\( d \)[/tex] dollars.
- To find the total cost, you multiply the number of peaches [tex]\( p \)[/tex] by the cost per peach [tex]\( d \)[/tex].
3. Establishing the Relationship:
- The relationship between the total cost [tex]\( t \)[/tex], the number of peaches [tex]\( p \)[/tex], and the cost per peach [tex]\( d \)[/tex] can be described by the equation:
[tex]\[
t = p \times d
\][/tex]
- This equation directly shows that the total cost [tex]\( t \)[/tex] is obtained by multiplying the number of peaches [tex]\( p \)[/tex] by the cost per peach [tex]\( d \)[/tex].
4. Choosing the Correct Option:
- Let's match this understanding with the given options:
- (a) [tex]\( t = p \times d \)[/tex]
- (b) [tex]\( p = t \times d \)[/tex]
- (c) [tex]\( t = p \)[/tex]
- (d) [tex]\( t = \frac{p}{d} \)[/tex]
5. Identifying the Correct Answer:
- Option (a) [tex]\( t = p \times d \)[/tex] matches our derived equation perfectly. Therefore, this is the correct option.
Hence, the equation that represents the relationship between the total cost [tex]\( t \)[/tex] and the number of peaches [tex]\( p \)[/tex] at the cost of [tex]\( d \)[/tex] dollars per peach is:
[tex]\[
\boxed{t = p \times d}
\][/tex]
