Question 68860
What is asked in the problem?
How many of dimes and quarters are there.
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Given:
Collection of dimes and quarters is worth $6.75.
The number of dimes is 4 less than 3 times the number of quarters.
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Representation:
Let x = number of quarters.
    y = number of quarters.
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Rewrite the given sentences to mathematical equation. 
The number of dimes is 4 less than 3 times the number of quarters.
x = 3y - 4
Collection of dimes and quarters is worth $6.75.
0.10x + 0.25y = $6.75 --> 10x + 25y = 675. You can multiply 100 each term so that we will not deal with decimals.
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Solve the two equation using Substitution Method. 
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Here are the Steps using Substition method

1. In either equation, solve for one variable in terms of the other.
x = 3y - 4
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2. Substitute for that variable in the other equation. Solve y.
10x + 25y = 675
10(3y - 4) + 25y = 675
30y - 40 + 25y = 675
55y = 715
y = 13 ----> number of quarters
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3. Substitute the result from step 2 in either equation. Solve for the other variable.
x = 3y - 4 , y = 13
x = 3(13) - 4
x = 39 - 4
x = 35 -----> number of dimes
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4. Check the solution in both original equations.
0.10x + 0.25y = $6.75 , x = 35, y = 13
0.10(35) + 0.25(13) = $6.75 
$3.50 + $3.25 = $6.75
$6.75 = $6.75 --------------->> True

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x = 3y - 4 , x = 35, y = 13
35 = 3(13) - 4
35 = 39 - 4
35 = 35 ---------->> True

<br> Therefore, the number of dimes are 35 and quarters 13.