Answer:
There are 52 dimes and 18 nickles
Step-by-step explanation:
Lets call x= number of dimes and y= number of nickles
then we have the first equation
(1) x + y = 70
As a nickel is worth 0.05 US$ and a dime is worth 0.10 US$, we have the second equation
(2) 0.10x + 0.05y = 6.10
We then have a linear system of 2 equations and 2 unknowns
(1) x +y = 70
(2) 0.10x + 0.05y = 6.10
In order to solve the system by the elimination method, we have to multiply on of the equations by a suitable number to eliminate one unknown when adding the two equations.
There are several ways of doing this. We could, for example, multiply (1) by -0.05 and then add it to (2)
(1) -0.05x – 0.05y = (-0.05)70
(2) 0.10x + 0.05y = 6.10
That is to say,
(1) -0.05x – 0.05y = -3.5
(2) 0.10x + 0.05y = 6.10
Adding (1) and (2) we get
-0.05x = -2.6 => x = (-2.6)/(-0.05) = 52 => x = 52
So we have 52 dimes.
Substituting this value in equation 1, we obtain
y = 70 - x = 70 – 52 = 18
Then we have 18 nickels
