Peter had 48 quarters and 11 dimes
<h3>Further explanation</h3>
Simultaneous Linear Equations could be solved by using several methods such as :
- <em>Elimination Method</em>
- <em>Substitution Method</em>
- <em>Graph Method</em>
If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.
Let us tackle the problem!
Let :
<em>Number of quarters ( 25 cent coins ) = x</em>
<em>Number of dimes ( 10 cent coins ) = y</em>
<em>When he counted his quarters and dimes, he found they had a total value of $13.10.</em>
<h2>0.25x + 0.10y = 13.10</h2>
<em>The number of quarters was 15 more than 3 times the number of dimes.</em>
<h2>x = 15 + 3y</h2>
If we would like to use the Substitution Method , then second equations above could be substituted into first equations.
0.25x + 0.10y = 13.10
0.25 (15 + 3y) + 0.10y = 13.10
3.75 + 0.75y + 0.10y = 13.10
0.85y = 13.10 - 3.75
0.85y = 9.35
y = 9.35 / 0.85
<h3>
y = 11</h3>
At last , we could find the value of x by substituting this y value into one of the two equations above :
x = 15 + 3y
x = 15 + 3(11)
x = 15 + 33
<h3>x = 48</h3>
<h3>Learn more</h3>
<h3>Answer details</h3>
Grade: High School
Subject: Mathematics
Chapter: Simultaneous Linear Equations
Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations