The ratio of dimes to nickels is 2/3. He has $.75 innickels. How many dimes does he have?
2/x = 3/15
3x = 30
x = 10 dimes
To find the number of dimes, we need to determine the total value of the nickels and compare it to the ratio. From the given information, we know that the ratio of dimes to nickels is 2/3, and the total value of the nickels is $0.75.
Let's start by finding the value of one nickel. Since he has $0.75 in nickels, we can divide $0.75 by the number of nickels he has.
Value of one nickel = $0.75 ÷ (number of nickels)
Now, let's calculate the value of one nickel:
Value of one nickel = $0.75 ÷ (number of nickels) = $0.75 ÷ (1/3)
To divide by a fraction, we can multiply by its reciprocal:
Value of one nickel = $0.75 × (3/1) = $2.25
So, the value of one nickel is $2.25.
Next, since the ratio of dimes to nickels is 2/3, we can set up the following equation to find the number of dimes:
Number of dimes / Number of nickels = 2/3
We know that the value of one nickel is $2.25. Let's use this information to rewrite the equation:
Number of dimes / $2.25 = 2/3
To solve for the number of dimes, we can cross-multiply:
Number of dimes = ($2.25 × 2) / 3
Number of dimes = $4.50 / 3
Number of dimes = 1.50
Since you can't have 1.50 dimes, we round down to the nearest whole number:
Number of dimes = 1
Therefore, he has 1 dime.
To find the number of dimes, we can set up a proportion using the given ratio.
Let's assume the number of dimes is represented by "x". According to the ratio, the number of nickels would be (2/3) times the number of dimes, which is (2/3)x.
We are also given that the amount of money in nickels is $0.75. Since each nickel is worth $0.05, we can set up an equation:
0.05 * (2/3)x = 0.75
To solve for x, we can multiply both sides of the equation by 3/2 (the reciprocal of 2/3):
(3/2)(0.05)(2/3)x = (3/2)(0.75)
0.05x = 1.125
Dividing both sides of the equation by 0.05:
x = 1.125 / 0.05
x = 22.5
Since we can't have a fraction of a dime, we need to round down to the nearest whole number.
Therefore, he has 22 dimes.