Question

Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question. A jar contains 70 nickels and dimes worth $6.10. How many of each kind of coin are in the jar? nickels dimes

Answer 1

There are 52 dimes and 18 nickles

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