Question 68860: A collection of quarters and dimes is worth $6.75. The number of dimes is 4 less than three times the number of quarters. How many of each are there?
I am confused as to how I would write this out, and solve it.
Please help.
Answer by rmromero(383)   (Show Source):
You can put this solution on YOUR website! What is asked in the problem?
How many of dimes and quarters are there.
Given:
Collection of dimes and quarters is worth $6.75.
The number of dimes is 4 less than 3 times the number of quarters.
Representation:
Let x = number of quarters.
y = number of quarters.
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.
Solve the two equation using Substitution Method.
Here are the Steps using Substition method
1. In either equation, solve for one variable in terms of the other.
x = 3y - 4
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
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
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
x = 3y - 4 , x = 35, y = 13
35 = 3(13) - 4
35 = 39 - 4
35 = 35 ---------->> True
Therefore, the number of dimes are 35 and quarters 13.
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