Respuesta :
Answer:
There are 10 dimes and 7 quarters of coins in all she have.
Step-by-step explanation:
Given:
Lily has $2.75 in her pocket, consisting of dimes and quarters.
There are 17 coins in all.
Now, to find the number of coins each she have.
Let the dimes be [tex]x.[/tex]
And the quarters be [tex]y.[/tex]
So, the total number of coins:
[tex]x+y=17.[/tex].......(1)
[tex]x=17-y.[/tex]
The value of a dime = $0.10.
And the value of a quarter = $0.25.
Now, the total money Lily has in her pocket:
[tex]0.10x+0.25y=2.75.[/tex]
Putting the value in the place of [tex]x[/tex] we get:
[tex]0.10(17-y)+0.25y=2.75[/tex]
⇒ [tex]1.7-0.10y+0.25y=2.75[/tex]
⇒ [tex]1.7+0.15y=2.75[/tex]
Subtracting both sides by 1.7 we get:
⇒ [tex]0.15y=1.05[/tex]
Dividing both sides by 0.15 we get:
⇒ [tex]y=7.[/tex]
The number of quarters = 7.
Now, putting the value of [tex]y[/tex] in equation (1) we get:
[tex]x+y=17.[/tex]
[tex]x+7=17.[/tex]
Subtracting both sides by 7 we get:
⇒ [tex]x=10.[/tex]
The number of dimes = 10.
Therefore, there are 10 dimes and 7 quarters of coins in all she have.
