Ms.lynch has 21 coins in nickles and dimes.Their total value is $1.65. How many of each coin does she have?
21 - ( 0.05x + 0.10x)=1.50
21- 0.15x = 1.50
0.15x=21-1.50
0.15x=19.5
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0.15 = 19.5/ 0.15
x=130 ??????
Your equation makes no sense to me at all
An equation only is useful and meaningful if the variable has been defined.
Let the number of nickels be x
then the number of dimes is 21-x
Now for the value of those coins:
5x + 10(21-x) = 165
5x + 210 - 10x = 165
-5x = -45
x = 9
then 21-x = 12
So we have 9 nickels and 12 dimes.
check:
do I have a total of 21 coins ? YES
value of my coins
= 5(9) + 10(12) = 165
All is good!
To solve this problem, we can set up a system of equations.
Let's say that Ms. Lynch has x nickels and y dimes.
The value of each nickel is $0.05, so the total value of nickels is 0.05x.
The value of each dime is $0.10, so the total value of dimes is 0.10y.
From the given information, we know that Ms. Lynch has a total of 21 coins and the total value of all these coins is $1.65.
Based on this, we can set up the following system of equations:
Equation 1: x + y = 21 (since Ms. Lynch has a total of 21 coins)
Equation 2: 0.05x + 0.10y = 1.65 (since the value of all nickels and dimes together is $1.65)
Now we can solve this system of equations to find the values of x and y.
To eliminate the decimal points in Equation 2, we can multiply all terms by 100:
0.05x + 0.10y = 1.65 becomes:
5x + 10y = 165
Now we can solve this system of equations using the method of substitution or elimination.
Let's solve it using the elimination method:
Multiply Equation 1 by 5:
5(x + y) = 5(21) becomes:
5x + 5y = 105
Now we have the following system of equations:
5x + 5y = 105
5x + 10y = 165
Subtract the first equation from the second equation to eliminate x:
(5x + 10y) - (5x + 5y) = 165 - 105:
5y = 60
y = 60/5
y = 12
Now we can substitute the value of y into Equation 1 to solve for x:
x + 12 = 21
x = 21 - 12
x = 9
Therefore, Ms. Lynch has 9 nickels and 12 dimes.