Whitney has 20 coins in her purse. Some are quarters and some are dimes. The total value of the coins is $3.35. How many quarters does Whitney have?
d+q = 20
10d+25q = 335
solve for q.
To solve this problem, we need to set up two equations based on the given information:
Let's say the number of quarters Whitney has is represented by 'q', and the number of dimes is represented by 'd'.
1. The first equation reflects the total number of coins:
q + d = 20
2. The second equation represents the total value of the coins in dollars:
0.25q + 0.10d = 3.35
To solve this system of equations, we can use substitution or elimination.
Let's use the elimination method. To do this, we will multiply both sides of the first equation by 0.10 to make the coefficient of 'd' the same in both equations:
0.10(q + d) = 0.10(20)
0.10q + 0.10d = 2
Now, we can subtract the new equation (2) from equation (3) to eliminate 'd':
(0.25q + 0.10d) - (0.10q + 0.10d) = 3.35 - 2
0.25q - 0.10q = 1.35
Combine like terms:
0.15q = 1.35
Divide both sides by 0.15:
q = 1.35 / 0.15
q = 9
Therefore, Whitney has 9 quarters.