Question

Wrote a system of equation to solve each problem ?

Answer 1

Answer:

Explanation:

Let us call x the number of dimes and y the number of quarters. We are told that there are a total of 110 coins and it means that

$x+y=110$

Furthermore, we also know that 1 dime = $0.10 and 1 quarter = $0.25; therefore, the worth of x dimes is $0.10 x and similarly, the worth of y quarters is $0.25. Therefore, if you sum them up ( dimes and quarters) their total worth will be

$0.10x+0.25y=20.30$

Now e have two equations and two unknowns and we solve for x by substitution.

Solving for x in the first equation gives

$0.10(110-y)+0.25y=20.30$

putting it into the second equation gives

Expanding the left-hand side gives

$11-0.10y+0.25y=20.30$$11+0.15y=20.30$$0.15y=9.3$$\boxed{y=62}$

Therefore, cassie has 62 quarters. To find the number of dimes, we solve

$x+y=110$$x+62=110$$\boxed{x=48.}$

Cassie has 48 dimes.

Hence we conclude that cassie has 62 quarters and 48 dimes.