Answer:
[tex]16[/tex] is the number of quarters and [tex]14[/tex] is the number of dimes
Step-by-step explanation:
we know that
[tex]1\ dime=\$0.10[/tex]
[tex]1\ quarter=\$0.25[/tex]
Let
x-----> the number of dimes
y------> the number of quarters
we know that
[tex]0.10x+0.25y=5.40[/tex] -----> equation A
[tex]x+y=30[/tex] ----Isolate the variable y
[tex]y=30-x[/tex] -----> equation B
Substitute equation B in equation A
[tex]0.10x+0.25(30-x)=5.40[/tex]
[tex]0.10x+7.5-0.25x=5.40[/tex]
[tex]0.25x-0.10x=7.5-5.40[/tex]
[tex]0.15x=2.1[/tex]
[tex]x=14\ dimes[/tex]
Find the value of y
[tex]y=30-x[/tex]
[tex]y=30-14=16\ quarters[/tex]
therefore
[tex]16[/tex] is the number of quarters and [tex]14[/tex] is the number of dimes
