Answer:
13 quarters.
Step-by-step explanation:
Let d represent number of dimes and q represent number of quarters.
We have been given that the number of quarters is 6 more than the number of dimes. We can represent this information in an equation as:
[tex]q=d+6...(1)[/tex]
We know that value of one dime is $0.10, so value of d dimes would be [tex]0.10d[/tex].
We know that value of one quarter is $0.25, so value of q quarters would be [tex]0.25q[/tex].
We have been given that Sally gave her brother $3.95 in quarters and dimes. We can represent this information in an equation as:
[tex]0.10d+0.25q=3.95...(2)[/tex]
Now, we have a system of linear equation and we will solve our system by substitution method.
From equation (1), we will get:
[tex]q-6=d[/tex]
Upon substituting this value in equation (2), we will get:
[tex]0.10(q-6)+0.25q=3.95[/tex]
[tex]0.10q-0.60+0.25q=3.95[/tex]
[tex]0.35q-0.60=3.95[/tex]
[tex]0.35q-0.60+0.60=3.95+0.60[/tex]
[tex]0.35q=4.55[/tex]
[tex]\frac{0.35q}{0.35}=\frac{4.55}{0.35}[/tex]
[tex]q=13[/tex]
Therefore, Sally gave her brother 13 quarters.
