how many dimes and quarters does jill have if she has $9.90 in dimes and quarters and she has 3 times as many dimes as quarters?
D = 3Q
10D + 25Q = 990
Substitute 3Q for D in second equation and solve for Q. Insert that value into the first equation and solve for D. Check by inserting both values into the second equation.
To find the number of dimes and quarters that Jill has, we can set up a system of equations.
Let's assume that Jill has x quarters. Since she has 3 times as many dimes as quarters, she would have 3x dimes.
Since the value of each quarter is $0.25, the total value of quarters in dollars would be 0.25x. Similarly, the total value of dimes in dollars would be 0.10(3x) = 0.30x.
According to the given information, the total value of dimes and quarters Jill has is $9.90, so we can write the equation:
0.25x + 0.30x = 9.90
To solve this equation, we can combine the like terms:
0.55x = 9.90
Now, we can isolate x by dividing both sides of the equation by 0.55:
x = 9.90 / 0.55
Calculating this, we find that x = 18.
Therefore, Jill has 18 quarters (x) and 3(18) = 54 dimes.