SOLUTION: A stack of dimes and a stack of quarters total $6.80
in value. There are a total of 41 coins. Determine the
number of dimes and the number of quarters in the
stacks.
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-> SOLUTION: A stack of dimes and a stack of quarters total $6.80
in value. There are a total of 41 coins. Determine the
number of dimes and the number of quarters in the
stacks.
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Question 1029975: A stack of dimes and a stack of quarters total $6.80
in value. There are a total of 41 coins. Determine the
number of dimes and the number of quarters in the
stacks. Found 2 solutions by Edwin McCravy, josmiceli:Answer by Edwin McCravy(20060) (Show Source):
Let the number of dimes be x
Let the number of quarters be y
Value Value
Type Number of of
of of EACH ALL
coin coins coin coins
-------------------------------------------
dimes x $0.10 $0.10x
quarters y $0.25 $0.25y
-------------------------------------------
TOTALS 41 ----- $6.80
The first equation comes from the "Number of coins" column.
x + y = 41
The second equation comes from the last column.
0.10x + 0.25y = 6.80
Get rid of decimals by multiplying every term by 100:
10x + 25y = 680
So we have the system of equations:
.
We solve by substitution. Solve the first equation for y:
x + y = 41
y = 41 - x
Substitute (41 - x) for y in 10x + 25y = 680
10x + 25(41 - x) = 680
10x + 1025 - 25x = 680
-15x + 1025 = 680
-15x = -345
x = 23 = the number of dimes.
Substitute in y = 41 - x
y = 41 - (23
y = 18 quarters.
Checking: 23 dimes is $2.30 and 18 quarters is $4.50
That's 41 coins.
And indeed $2.30 + $4.50 = $6.8
Edwin
You can put this solution on YOUR website! Let = number of dimes
Let = number of quarters
----------------------------
(1)
(2) ( in cents )
-------------------------
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)
-----------------------
and
(1)
(1)
----------------
There are 23 dimes and 18 quarters
----------------
check:
(2)
(2)
(2)
(2)
OK
