word problems

Question

Junior has a collection of thirty quarters and dimes in his piggy bank. If Junior has $6.00 in his piggy bank, how many quarters and dimes are in the collection?

Answer 1

Let q be the number of quarters in his piggy bank

 

Then 30 - q is the number of dimes.

 

The total value of the quarters is .25q

 

The total value of the dimes is .10(30 - q)

 

Add these together and set them equal to 6.00:

 

.25q + .10(30 - q) = 6.00

 

Solve for q to get the number of quarters.  Then you can easily determine the number of dimes.

 

 

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Answer 2

Let x = the number of quarters Junior has and let y = the number of dimes he has. Assuming that the problem is stating that Junior has a total of 30 coins, then we know that:

 

x + y = 30

 

We also know that the value of the coins can be expressed as:

 

.25x + .10y = 6

 

We can multiply both sides by 100 to clear decimals from the above equation.

 

25x + 10y = 600

 

We know have a system of two equations, which can be solved using either the Substitution Method or the Elimination Method. Let's choose the Substitution Method. We can solve the first equation for y.

 

y = 30 - x

 

Now, replace every instance of y in the second equation with (30 - x).

 

25x + 10(30 - x) = 600

 

You should now be able to solve this linear equation for x, which will then allow you to determine the number of quarters and dimes that Junior has.