Answer:
There are 90 coins in the bag.
Step-by-step explanation:
Let [tex]x[/tex], [tex]y[/tex] the number of dimes and quarters. Now we proceed to translate each relevant sentence into mathematical expressions:
(i) The number of quarters is 6 more than twice the number of dimes:
[tex]y = 2\cdot x + 6[/tex] (1)
(ii) There are a total of 276 coins in the bag:
[tex]x + y = 276[/tex] (2)
By applying (1) in (2), we find that the number of dimes is:
[tex]x+2\cdot x + 6 = 276[/tex]
[tex]3\cdot x = 270[/tex]
[tex]x = 90[/tex]
There are 90 coins in the bag.
