Sam has a total of 200 dimes and quarters. If the total value of the coins is $28.10, how many quarters does he have?
what is the value of 200 dimes? Subtract the answer from $28.10. How many quarters in your answer?
Hmm. Interesting. But if he has 200 dimes, then he would have 0 quarters. I think the interpretation is supposed to be 200 (dimes and quarters), not (200 dimes) and quarters. Besides, you can't make up $8.10 with just quarters.
How about:
d+q = 200
10d+25q = 2810
d = 146
q = 54
check:
14.60 in dimes + 13.50 in quarters = 28.10
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that Sam has x number of quarters and y number of dimes.
We know that Sam has a total of 200 dimes and quarters, so we can write the first equation as:
x + y = 200
We also know that the total value of the coins is $28.10. Since a quarter is worth $0.25 and a dime is worth $0.10, we can write the second equation as:
0.25x + 0.10y = 28.10
Now, we can use these equations to solve for x, which represents the number of quarters Sam has.
We can start by multiplying the first equation by -0.10:
-0.10x - 0.10y = -20
Adding this equation to the second equation, we eliminate the variable y:
0.25x - 0.10x - 0.10y + 0.10y = 28.10 - 20
0.15x = 8.10
Dividing both sides of the equation by 0.15, we find:
x = 8.10 / 0.15
x = 54
Therefore, Sam has 54 quarters.