Answer:
35 dimes and 60 nickels
Step-by-step explanation:
let d = # of dimes and n = # of nickels
We know that Timmy has a total of 95 coins, consisting of dimes and nickels
So d + n = 95
The total value of his bank is $6.50
A dime is worth $0.10 and a nickel is work $0.05
So 0.10d + 0.05n = $6.50
Note that we've just created a system of equations that we can solve
We have the two equations
0.10d + 0.05n = 6.50 and d + n = 95
There are many different methods we can use to solve this system but the easiest way in this situation is probably going to be the substitution method.
First we are going to want to rearrange the terms of the second equations so that one of the variables are defined.
d + n = 95
- subtract d from both sides -
n = 95 - d
We now defined "n"
Now that we have defined one of the variables we can plug in ( or substitute ) the value of it into the other equation. Once we substitute it we can solve for the other variable.
0.10d + 0.05n = 6.50
n = 95 - d
0.10d + 0.05(95 - d) = 6.50
we now solve for d
0.10d + 0.05(95 - d) = 6.50
step 1 distribute the 0.05
0.05 * 95 = 4.75 and 0.05 * -d = -0.05d
0.10d + 4.75 - 0.05d = 6.50
step 2 combine like terms 0.10d - 0.05d = 0.05d
0.05d + 4.75 = 6.50
step 3 subtract 4.75 from both sides
0.05d = 1.75
step 4 divide both sides by 0.05
0.05d / 0.05 = d and 1.75 / 0.05 = 35
d = 35
Now that we have found the value of one variable we can plug it into one of the equations and solve for the other variable ( note that the equation that we use does not matter, we will acquire the same answer )
d + n = 95
d = 35
35 + n = 95
subtract 35 from both sides
n = 60
We can conclude that he has 35 dimes and 60 nickels
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