Question

Rough SOE Booklet

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Marcy has a total and of 100 dimes and quarters. If the value of the coins $14.05, how many quarters does she have ?

Answer 1

Answer: She has 27 quarters.

Explanation:

Let be "d" the number of dimes Marcy has and "q" the number of quarters Marcy has.

Based on the information provided in the exercise, we can set up the following system of equations:

`\left \{ {{d+q=100} \atop {0.1d+0.25q=14.05}} \right.`

In order to solve the system of equations, we can use the Elimination method:

1. Multiply the first equation by -0.1
2. Add the equations.
3. Solve for "q".

Then:

`\left \{ {{-0.1d-0.1q=-10} \atop {0.1d+0.25q=14.05}} \right.\\............................\\0.15q=4.05\\\\q=(4.05)/(0.15)\\\\q=27`