Jason has $2.25 worth of dimes and quarters. He has twice as many dimes as quarters. Determine the number of dimes and the number of quarters that Jason has.
d = numbers of dimes
q = numbers of quarters
1 dime = 10 cents = $ 0.1
1 quarter = 25 cents = $ 0.25
Jason has $2.25 means:
0.1 d + 0.25 q = 2.25
He has twice as many dimes as quarters means:
d = 2 q
Put this value in equation:
0.1 d + 0.25 q = 2.25
0.1 ∙ 2 q + 0.25 q = 2.25
0.2 q + 0.25 q = 2.25
0.45 q = 2.25
q = 2.25 / 0.45 = 5
d = 2 q = 2 ∙ 5 = 10
10 dimes and 5 quarters
10 ∙ $ 0.1 + 5 ∙ $ 0.25 = $ 1 + $ 1.25 = $ 2.25
To determine the number of dimes and quarters that Jason has, we need to set up a system of equations.
Let's denote the number of quarters as 'q' and the number of dimes as 'd'.
From the given information, we know that Jason has twice as many dimes as quarters, so we can write the equation:
d = 2q
We are also given that the total value of Jason's dimes and quarters is $2.25. Since each dime is worth $0.10 and each quarter is worth $0.25, we can write the equation for the total value as:
0.10d + 0.25q = 2.25
Now we can solve this system of equations.
Substitute the value of d from the first equation into the second equation:
0.10(2q) + 0.25q = 2.25
Simplify:
0.20q + 0.25q = 2.25
0.45q = 2.25
Divide by 0.45 to solve for q:
q = 2.25 / 0.45
q = 5
Now substitute the value of q into the first equation to find the number of dimes:
d = 2(5)
d = 10
Therefore, Jason has 10 dimes and 5 quarters.
Let's represent the number of quarters as q.
Since Jason has twice as many dimes as quarters, the number of dimes can be represented as 2q.
The total value of the quarters can be calculated as 0.25q.
The total value of the dimes can be calculated as 0.10(2q) = 0.20q.
We can set up the equation: 0.25q + 0.20q = 2.25.
Combining like terms, we have 0.45q = 2.25.
Dividing both sides of the equation by 0.45, we get q = 5.
So, Jason has 5 quarters.
The number of dimes can be calculated as 2q = 2(5) = 10.
Therefore, Jason has 10 dimes.
In summary, Jason has 10 dimes and 5 quarters.