Answer:
The question is incorrect but if half nickels and quarters exist then you could say the answer is 7.5 nickels and 6.5 quarters.
The problem:
14 coins that are either nickels are quarters
The total dollar amount of these coins is 2 dollars
Step-by-step explanation:
Let n be the number of nickels.
Let q be the number of quarters.
We are given that n+q=14 and that .05n+.25q=2.
I'm going to choose to solve the system by elimination.
Multiplying the first equation by .25 gives:
.25n+.25q=.25(14)
.25n+.25q=3.5
So let's line the equations up now:
.25n+.25q=3.5
.05n+.25q=2
---------------------If we subtract the equations, the variable q will be eliminated. Thus, we will able to solve for the variable n.
.20n+0q=1.5
.20n=1.5
Dividing both sides by .2 gives:
n=7.5
If n=7.5 and n+q=14, then we have 7.5+q=14 by substitution property.
We can subtract 7.5 on both sides giving us:
q=14-7.5=6.5
We cannot have 7.5 nickels and 6.5 quarters but this satisfies the given information.
Check:
7.5+6.5=(7+6)+(.5+.5)=13+1=14
7.5(.05)+6.5(.25)=2
Now, the requested way which is by substitution:
Let n be the number of nickels.
Let q be the number of quarters.
We are given that n+q=14 and that .05n+.25q=2.
We can solve the first equation for either n or q and then substitute that into the other equation allowing us to solve for the other variable.
Let's solve for q by subtraction n on both sides:
q=14-n
We are going to replace q in the second equation with (14-n) giving us:
.05n+.25(14-n)=2
Distribute:
.05n+3.5-.25n=2
Combine like terms:
-0.2n+3.5=2
Subtract 3.5 on both sides:
-0.2n=-1.5
Divide both sides by -0.2:
n=7.5
Since q=14-n and n=7.5, then q=14-7.5=6.5 .
We are already check the solution above.
