Answer:
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:
[tex]Q\,0.25+D\,0.10 = 9.45[/tex]
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:
[tex]D=60-Q\\\\0.25\,Q+0.10\,D = 9.45\\0.25\,Q+0.10\,(60-Q) = 9.45\\0.25\,Q+6-0.1Q=9.45\\0.25\, Q-0.1\,Q=9.45-6\\0.15\,Q=3.45\\Q=\frac{3.45}{0.15} \\\\Q=23[/tex]
Then, there are 23 quarters in the collection. We can find the number of dimes via the substitution equation we used:
[tex]D=60-Q\\D=60-23\\D=37[/tex]
