Notice the the collection of quarters and dimes consists of 90 coins. We don't know the number of each type of coin, so they are our UNKNOWNS. We name them "q" and "d".
We can then write our first equation:
q + d = 90 (for the total of 90 coins)
The second equation we write involves the values. Recall that a quarter is $0.25 and that a dime is $0.10
so we write the addition of the individual values for our coins totalling $12 as:
0.25 q + 0.1 d = 12
Now we solve for d in the first equation: d = 90 - q
and use this expression to substitute for "d" in the second equation as shown below:
0.25 q + 0.1 (90 - q) = 12
use distributive property to remove the parenthesis
0.25 q + 9 - 0.1 q = 12
combine like terms:
0.15 q + 9 = 12
subtract 9 from both sides
0.15 q = 12 - 9 = 3
divide bith sides by 0.15 in order to isolate/solve for q
q = 3 / 0.15
q = 20
Therefore, if the number of quarters is 20, then the number of dimes must be:
d = 90 - 20 = 70
Answer: The collection consists of 20 quarters and 70 dimes.