heather has $2.50 in nickels, dimes, and quarters. she has 3 times as many nickels as dimes and four times as many quaters as dimes
number of dimes -- x
number of nickels -- 3x
number of quarters -- 4x
10x + 5(3x) + 25(4x) = 250
solve for x , then sub in my definitions
Nickels:6
Dimes:2
Quarters:8
To solve this problem, let's assign variables to the unknown quantities:
Let's say the number of dimes Heather has is "d".
Therefore, the number of nickels she has is 3 times the number of dimes, which is 3d.
And the number of quarters she has is four times the number of dimes, which is 4d.
Now, let's convert the information given into equations:
The value of the nickels: 0.05 * (3d)
The value of the dimes: 0.10 * d
The value of the quarters: 0.25 * (4d)
According to the problem, the total value of all the coins is $2.50. So, we can set up an equation:
0.05 * (3d) + 0.10 * d + 0.25 * (4d) = 2.50
Now, let's solve the equation to find the value of "d" and then calculate the number of nickels and quarters:
0.15d + 0.10d + 1.00d = 2.50
0.25d = 2.50
d = 2.50 / 0.25
d = 10
Therefore, Heather has 10 dimes. Now let's substitute this value back into the expressions we established earlier:
The number of nickels: 3d = 3 * 10 = 30 nickels
The number of quarters: 4d = 4 * 10 = 40 quarters
So, Heather has 30 nickels, 10 dimes, and 40 quarters.