Gabe has 60 coins consisting of quarters and dimes. The combined value of the coins is $9.45. How many quarters and dimes does Gabe have?

There are 23 quarters and 37 dimes in the collection

Step-by-step explanation:

Let's name the two unknowns we need to find :

Q = number of quarters in the collection

D = number of dimes in the collection

So our first equation on the number of coins we have in the collection can be written as:

Q + D = 60

Now let's write an equation that takes care of the total value of the collection ($ 9.45), having in mind that each quarter is worth $ 0.25, and each dime is $ 0.10:

So let's solve this system of linear equations in "Q" and "D" by substitution. We use the first equation to solve for "d" for example, and then use this to substitute for D in the second equation:

Then, there are 23 quarters in the collection. We can find the number of dimes via the substitution equation we used:

$649.60

step-by-step explanation: