A bag of coins contains only quarters and dimes. The number of dimes in the bag can be represented by x. The number of quarters is 6 more than twice the number of dimes. There a…

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asked Oct 18, 2021 30.9k views

1 Answer

Scifirocket · Answer 1 · 2021-10-25T13:53:51+0000

Answer:

There are 90 coins in the bag.

Explanation:

Let
,
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:

$y = 2\cdot x + 6$ (1)

(ii) There are a total of 276 coins in the bag:

x + y = 276 (2)

By applying (1) in (2), we find that the number of dimes is:

$x+2\cdot x + 6 = 276$

$3\cdot x = 270$

x = 90

There are 90 coins in the bag.