Bobby is bringing his collection of dimes and quarters to the bank to deposit into his savings account. If [tex]\( d \)[/tex] represents the number of dimes in Bobby's collection, [tex]\( q \)[/tex] represents the number of quarters, and the collection is worth [tex]\(\$63.75\)[/tex], which of the following equations models the value of Bobby's collection?
A. [tex]\( 63.75 = d + q \)[/tex] B. [tex]\( 63.75 = 25d + 10q \)[/tex] C. [tex]\( 63.75 = 10d + 25q \)[/tex] D. [tex]\( 63.75 = 0.10d + 0.25q \)[/tex]
Let's determine the correct equation that models the value of Bobby's collection given he has [tex]$d$[/tex] dimes and [tex]$q$[/tex] quarters, and the total value is [tex]$63.75.
1. First, understand the value of each type of coin:
- Each dime is worth $[/tex]0.10. - Each quarter is worth [tex]$0.25.
2. Next, the total value of Bobby's dimes and quarters can be expressed as:
- The value of d dimes: \( 0.10 \times d \).
- The value of q quarters: \( 0.25 \times q \).
3. Since the total value of Bobby's collection is $[/tex]63.75, we can write the equation that combines these values:
[tex]\[ 0.10d + 0.25q = 63.75 \][/tex]
Let's now evaluate each given option to identify the correct one:
- Option A: [tex]\( 63.75 = d + q \)[/tex]
This implies that the total number of coins equals 63.75, which is incorrect because it does not account for the different values of dimes and quarters.
- Option B: [tex]\( 63.75 = 25d + 10q \)[/tex]
This equation implies that a dime is worth [tex]$25 and a quarter is worth $[/tex]10, which is not correct.
- Option C: [tex]\( 63.75 = 10d + 25q \)[/tex]
This suggests that a dime is worth [tex]$10 and a quarter is worth $[/tex]25, which again is incorrect.
