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Wrote a system of equation to solve each problem ?

Wrote a system of equation to solve each problem ?-example-1

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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.

User Hasanthi
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