Number of dimes collected by Rosalyn = [tex]250[/tex]
How to calculate the number of dimes by Rosalyn?
Let D = # of dimes , Q = # of quarter.
We have
A dime is [tex]10[/tex] pennies , a quarter is [tex]25[/tex] pennies and $[tex]82.50[/tex] is [tex]8250[/tex] pennies.
Now this leads to the equation:
[tex]10D + 25 Q =8250[/tex]
If Rosalyn collected [tex]50[/tex] more quarters than dimes,
Then [tex]Q=D+50[/tex]
[tex]10D+25(D+50)=8250[/tex]
[tex]35D+1250=8250[/tex]
[tex]35D=7000[/tex]
[tex]D=\frac{7000}{35}[/tex]
[tex]D = 200[/tex]
So there are [tex]200[/tex] dimes.
And since there are [tex]50[/tex] more quarters than dimes , hence there are [tex]250[/tex] quarters.
So Rosalyn collected [tex]250[/tex] dimes.
To learn more about the calculate the number of dimes visit:
https://brainly.com/question/12461707
#SPJ9
