Question

Wrote a system of equation to solve each problem ?

Answer 1

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.