SOLUTION: Jennifer has 15 coins worth a total of $1.45. All of the coins are nickels, dimes, or quarters. The number or quarters is 1/4 the number of nickels and dimes combined. Solve a line

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: Jennifer has 15 coins worth a total of $1.45. All of the coins are nickels, dimes, or quarters. The number or quarters is 1/4 the number of nickels and dimes combined. Solve a line      Log On

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Question 998423: Jennifer has 15 coins worth a total of $1.45. All of the coins are nickels, dimes, or quarters. The number or quarters is 1/4 the number of nickels and dimes combined. Solve a linear system to find how many of each kind of coin she has. Please help me... Thanks
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+n+ = number of nickels
+d+ = number of dimes
+q+ = number of quarters
-------------------------
(1) +n+%2B+d+%2B+q+=+15+
(2) +5n+%2B+10d+%2B+25q+=+145+
(3) +q+=+%281%2F4%29%2A%28+n+%2B+d+%29+
-------------------------
(3) +n+%2B+d+=+4q+
Substitute this into (1)
(1) +4q+%2B+q+=+15+
(1) +5q+=+15+
+q+=+3+
---------------
Multiply both sides of (1) by +5+
and subtract (1) from (2)
(2) +5n+%2B+10d+%2B+25q+=+145+
(1) +-5n+-+5d+-+5q+=+-75+
--------------------------
+5d+%2B+20q+=+70+
+5d+%2B+20%2A3+=+70+
+5d+=+10+
+d+=+2+
-------------
(1) +n+%2B+d+%2B+q+=+15+
(1) +n+%2B+2+%2B+3+=+15+
(1) +n+=+10+
--------------------
There are 10 nickels, 2 dimes, and 3 quarters
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check answers:
(2) +5n+%2B+10d+%2B+25q+=+145+
(2) +5%2A10+%2B+10%2A2+%2B+25%2A3+=+145+
(2) +50+%2B+20+%2B+75+=+145+
(2) +145+=+145+
-----------------
(3) +q+=+%281%2F4%29%2A%28+n+%2B+d+%29+
(3) 3+=+%281%2F4%29%2A%28+10+%2B2+%29+
(3) +3+=+%281%2F4%29%2A12+
(3) +3+=+3+
OK