Ayaana Buck

2021-09-02

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? ### Answer & Explanation broliY Skilled2021-09-03Added 97 answers 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.

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

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

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

$10\left(30-y\right)+25y$

$=510300-10y+25y$

$=51015y=210y$

$=14$

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.

Jeffrey Jordon