Ashley had an equal number of dimes and quarters until she gave 15 quarters away. She now has $ 22.50 in dimes and quarters. How many dimes does she have?
at start,
number of dimes --- x
number of quarters -- x
after give-away:
dimes = x
quarters = x-15
10x + 25(x-15) = 2250
solve for x
To find out how many dimes Ashley has, we can use algebra. Let's denote the number of dimes she originally had as 'x'. Since she had an equal number of dimes and quarters initially, she also had 'x' quarters.
Now, since she gave away 15 quarters, she now has 'x - 15' quarters left.
We need to calculate the total value of her remaining dimes and quarters, which is $22.50. The value of 'x' dimes is 10x cents and the value of 'x - 15' quarters is 25(x - 15) cents.
Since there are 100 cents in a dollar, we can write the equation:
10x + 25(x - 15) = 2250
Now we can solve this equation to find the value of 'x'.
10x + 25x - 375 = 2250
35x - 375 = 2250
35x = 2625
x = 75
So, Ashley originally had 75 dimes.