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Question 149206: Joe has a collection of nickels and dimes tha is worth$5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.45. How may dimes does he have? Please show all work...
So far all I can come up with is x =dimes, y= nickels.
x(2), y+8 =$10.45
: Joe has a collection of nickels and dimes tha is worth$5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.45. How may dimes does he have? Please show all work...
So far all I can come up with is x =dimes, y= nickels.
x(2), y+8 =$10.45

Answer by nerdybill(1129) About Me  (Show Source):
You can put this solution on YOUR website!
Hey, you already submitted this...
.
Here's your solution:
Let n = number of nickels
and d = number of dimes
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Because we have two unknowns we need two equations:
From: "Joe has a collection of nickels and dimes that is worth $5.65." we get
.05n + .10d = 5.65 (equation 1)
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From: "If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.45." we get:
.05(n+8) + .10(2d) = 10.45
.05n + .40 + .20d = 10.45
.05n + .20d = 10.05 (equation 2)
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n = 25 (nickels)
d = 44 (dimes)
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Below shows the details:
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
system( <BR> 0.05\n + 0.1\d = 5.65,<BR> 0.05\n + 0.2\d = 10.05 )<BR> We'll use substitution. After moving 0.1*d to the right, we get:
0.05*n = 5.65 - 0.1*d, or n = 5.65/0.05 - 0.1*d/0.05. Substitute that
into another equation:
0.05*(5.65/0.05 - 0.1*d/0.05) + 0.2\d = 10.05 and simplify:
EXPLAIN simplification of an expression
Your Result:
Simplify 0.05*(5.65/0.05-0.1*d/0.05)+0.2d=10.05
  • Solutions: d=44.
  • Graphical form: 0.05*(5.65/0.05-0.1*d/0.05)+0.2d=10.05 simplifies to 0=0
  • Text form: 0.05*(5.65/0.05-0.1*d/0.05)+0.2d=10.05 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon( 0.05*(5.65/0.05-0.1*d/0.05)+0.2d=10.05 )
    simplify_cartoon( 0.05*(5.65/0.05-0.1*d/0.05)+0.2d=10.05 )

Detailed explanation:

Look at 0.05*(highlight_red( 5.65 )/highlight_red( 0.05 )-0.1*d/0.05)+0.2*d=10.05.
Replaced numbers in term with 113
It becomes 0.05*(highlight_green( 113 )-0.1*d/0.05)+0.2*d=10.05.
Look at 0.05*(113-highlight_red( 0.1 )*d/highlight_red( 0.05 ))+0.2*d=10.05.
Replaced numbers in term with 2
It becomes 0.05*(113-highlight_green( 2 )*d)+0.2*d=10.05.
Look at 0.05*(highlight_red( 113 )-2*d)+0.2*d=10.05.
Moved 113 to the right of expression
It becomes 0.05*(-2*d+highlight_green( 113 ))+0.2*d=10.05.
Look at 0.05*(-2*d+113)+0.2*d=highlight_red( 10.05 ).
Moved these terms to the left highlight_green( -10.05 )
It becomes 0.05*(-2*d+113)+0.2*d-highlight_green( 10.05 )=0.
Look at highlight_red( 0.05*(-2*d+113) )+0.2*d-10.05=0.
Expanded term 0.05 by using associative property on (-2*d+113)
It becomes -highlight_green( 0.05*2*d )+highlight_green( 0.05*113 )+0.2*d-10.05=0.
Look at -0.05*2*d+highlight_red( 0.05*113 )+0.2*d-highlight_red( 10.05 )=0.
Replace constants in expression: highlight_red( 0.05*113 ),highlight_red( -10.05 ) with highlight_green( -4.4 )
It becomes highlight_green( -4.4 )-0.05*2*d+0.2*d=0.
Look at highlight_red( -4.4 )-0.05*2*d+0.2*d=0.
Moved -4.4 to the right of expression
It becomes -0.05*2*d+0.2*d+highlight_green( -4.4 )=0.
Look at -0.05*2*d+0.2*d+highlight_red( -4.4 )=0.
Removed extra sign in front of -4.4
It becomes -0.05*2*d+0.2*d-highlight_green( 4.4 )=0.
Look at -highlight_red( 0.05*2*d )+highlight_red( 0.2*d )-4.4=0.
Eliminated similar terms highlight_red( -0.05*2*d ),highlight_red( 0.2*d ) replacing them with highlight_green( (-0.05*2+0.2)*d )
It becomes highlight_green( (-0.05*2+0.2)*d )-4.4=0.
Look at (-highlight_red( 0.05*2 )+highlight_red( 0.2 ))*d-4.4=0.
Replace constants in expression: highlight_red( -0.05*2 ),highlight_red( 0.2 ) with highlight_green( 0.1 )
It becomes (highlight_green( 0.1 ))*d-4.4=0.
Look at highlight_red( (highlight_red( 0.1 ))*d )-4.4=0.
Remove unneeded parentheses around factor highlight_red( 0.1 )
It becomes highlight_green( 0.1 )*d-4.4=0.
Look at highlight_red( 0.1*d-4.4 )=0.
Solved linear equation highlight_red( 0.1*d-4.4=0 ) equivalent to 0.1*d-4.4 =0
It becomes highlight_green( 0 )=0.
Result: 0=0
Solutions: d=44.

Done!
So, we know that d=44. Since n = 5.65/0.05 - 0.1*d/0.05, n=25.

Answer: system( n=25, d=44 ).

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