No solution! Here's why:
Let the number of nickels be x
Then the number of dimes, using
ONE PART = TOTAL MINUS OTHER PART,
is 22-x.
Value Value
Type Number of of
of of EACH ALL
coin coins coin coins
-------------------------------------------
NICKELS x $0.05 $0.05x
DIMES 22-x $0.10 $0.10(22-x)
-------------------------------------------
TOTALS 22 ----- $2.35
The equation comes from the column on the right
0.05x + 0.10(22-x) = 2.35
Get rid of decimals by multiplying every term by 100
5x + 10(22-x) = 235
5x + 220 - 10x = 235
-5x + 220 = 235
-5x = 15
x = -3 = the number of nickels
The number of dimes is 22-x or 22-(-3) or 25 dimes.
Checking: -3 nickels is -$0.15 and 25 dimes is $2.50
And -$0.15+2.50 = $2.35.
However, the number of nickels cannot be negative, so
THERE IS NO SOLUTION.
Further reason for "no solution. Here are all the ways you
can have 22 coins in nickels and dimes. You can see that
none of them add up to $2.35. The most you can have is $2.15
and the least you can have is $1.15. So either you copied
the problem wrong o else the answer is "no solution".
1 nickel and 21 dimes is $2.15.
2 nickels and 20 dimes is $2.10.
3 nickels and 19 dimes is $2.05.
4 nickels and 18 dimes is $2.00.
5 nickels and 17 dimes is $1.95.
6 nickels and 16 dimes is $1.90.
7 nickels and 15 dimes is $1.85.
8 nickels and 14 dimes is $1.80.
9 nickels and 13 dimes is $1.75.
10 nickels and 12 dimes is $1.70.
11 nickels and 11 dimes is $1.65.
12 nickels and 10 dimes is $1.60.
13 nickels and 9 dimes is $1.55.
14 nickels and 8 dimes is $1.50.
15 nickels and 7 dimes is $1.45.
16 nickels and 6 dimes is $1.40.
17 nickels and 5 dimes is $1.35.
18 nickels and 4 dimes is $1.30.
19 nickels and 3 dimes is $1.25.
20 nickels and 2 dimes is $1.20.
21 nickels and 1 dime is $1.15.
Edwin
