# solve each problem by setting up and solving an appropriate system of equations.Cindy has 30 coins,consisting of dimes and quarters,that total $5.10 Ayaana Buck 2021-09-02 Answered solve each problem by setting up and solving an appropriate system of equations. Cindy has 30 coins, consisting of dimes and quarters, that total$5.10. How many coins of each kind does she have?

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broliY

Given :
The number of coins she have is 30 consisting of dimes and quarters. Total of
the coins is $5.10 To find : The number of coins of dimes and quarters. Let the number of dimes be x, and the number of quarters be y. Total number of coins she have is 30 consisting of dimes and quarters. $$x + y = 30$$ .........(1) Total number of coins is$5.10 convert into cents, that is 510 cents.

$$10 x + 25 y = 510$$ ............(2)

Solve equation (1) for x in terms of y. $$x = 30 - y$$

Substitute $$30 - y$$ for x in equation (2),

$$10 (30−y) + 25y$$

$$= 510 300 − 10y + 25 y$$

$$= 510 15 y = 210 y$$

$$= 14$$

Substitute $$y=14$$ in equation (2),

$$x + 14 = 30$$

$$x = 16$$

Thus, the number of dimes is 16 and the number of quarters is 14.

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