Answered

Rohan has quarters and nickels that altogether have a value of $1.95. The number of

nickels is three more than the number of quarters. How many nickels and how many

quarters does Rohan have?

nickel (s) and

quarter (s)

Verified Answer :

Answer:

Rohan has 6 quarters and 9 nickels

Step-by-step explanation:

Identifying the Equations Given

Rohan's total money value consisting of quarters and nickels that are valued at 0.25 and 0.05 respectively, in dollars, equals $1.95. This can be written as,

\(\rm 0.25q+0.05n=1.95\).

If Rohan's number of nickels is 3 more than the number of quarters he owns then the number of nickels he has is,

\(\rm n=3+q\).

Systems of Equations

If the problem asks for the number of nickels and quarters or n and q, then those equations must be used in a systems of equations to find their values.

Doing this allows us to find the value of one variable in which can be plugged back into either equation to find the value of the other variable.

Since in the second equation, n is in terms of q, we can use substitution to find the value of q!

\(\rm 0.25q+0.05n=1.95\\\\0.25q+0.05(3+q)=1.95\)

\(\rm 0.25q+0.15+0.05q=1.95\)     (distribute the 0.05)

\(\rm 0.3q+0.15=1.95\)  (combine like terms)

\(\rm 0.3q=1.8\)   (subtract 0.15 both sides)

\(\rm q= 6\)  (divide both sides by 0.3).

Recalling that Rohan's nickels are 3 more than his quarters, he must have 9 nickels!

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