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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?

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?

Answer:There are 23 quarters and 37 dimes in the collectionStep-by-step explanation:Let's name the two unknowns we need to find :Q = number of quarters in the collectionD = number of dimes in the collectionSo our first equation on the number of coins we have in the collection can be written as:Q + D = 60Now 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:...

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