A person has a bag containing quarters and dimes. There are a total of \( 155 \) coins in the bag, and the total value of the coins is \( \$ 21.50 \) . Determine how many quarters and dimes are in the bag. There are There are quarters.
Pregunta
Answer
\(d + q = 155,0.25 q + 0.1 d = 21.5 : q = 40 , d = 115 \)
There are 40 quarters
There are 115 dimes
Steps
\( \left[ \begin{array} { c } { d + q = 155 } \\ { 0.25 q + 0.1 d = 21.5 } \end{array} \right]\) Isolate \( d \) for \( d + q = 155 : d = 155 - q \)
Substitute \( d = 155 - q \)
\( [ 0.25 q + 0.1 ( 155 - q ) = 21.5 ]\) Simplify
\( [ 0.15 q + 15.5 = 21.5 ] \)
Isolate \( q \) for \( 0.15 q + 15.5 = 21.5 : q = 40\) For \( d = 155 - q \)
Substitute \( q = 40 \)
\( d = 155 - 40 \)
Simplify
\( d = 115 \)
The solutions to the system of equations are:
\( q = 40 , d = 115\)
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