To determine the correct equation that can be used to find [tex]\( d \)[/tex], the number of dollar coins Giuliana has, let's follow the step-by-step solution:
1. Let [tex]\( d \)[/tex] be the number of dollar coins.
2. Since there are 22 coins in total, the number of quarters is [tex]\( 22 - d \)[/tex].
3. The value of each dollar coin is [tex]$\$[/tex] 1[tex]$.
4. The value of each quarter is $[/tex]\[tex]$ 0.25$[/tex].
Now we'll form an equation based on the total value of the coins, which should equal [tex]$\$[/tex] 10.75$.
The value of the dollar coins:
[tex]\[
d \times 1 = d
\][/tex]
The value of the quarters:
[tex]\[
(22 - d) \times 0.25
\][/tex]
The total value of the coins:
[tex]\[
d + 0.25(22 - d) = 10.75
\][/tex]
Therefore, the correct equation is:
[tex]\[
0.25(22 - d) + d = 10.75
\][/tex]
