Algebraic word problems

Question

Katie has twice as many nickels as quarters. If the coins are worth $4.90, how many quarters does Katie have? How many nickels does Katie have?

Answer 1

Algebraic word problems

Katie has twice as many nickels as quarters. If the coins are worth $4.90, how many quarters does Katie have? How many nickels does Katie have?

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Sometimes you have to read word problems twice and slowly to properly understand the facts.

You have to use variables to represent the UNKNOWN values.

Let N = number of nickels

Let Q = number of quarters

1/2N = Q...OR...N=2Q

N(.05) + Q (.25) = 4.90

--------------------------You now have the famous system of 2 equations and 2 unknowns-----------

With the system of equations you can solve for one variable and substitute to find the other one.

Using the 1st equation, substitute the variable Q into the second equation like so......

N(.05) + .5N (.25) = 4.90

----EVALUATE THE EXPRESSION and ISOLATE the variable N to one side of the equation-----

.05N + .125N = 4.90

.175N = 4.90

N = 4.90/.175 = 28 NICKELS....and....Q = 1/2 N = 1/2 (28) = 14 QUARTERS

....check your work.....

N(.05) + Q (.25) = 4.90.....28 (.05) + 14 (.25) = 1.40 + 3.50 = 4.90....that checks out perfectly....