Sal keeps quarters, nickels, and dimes in his change jar. He has a total of 52 coins. He has three more quarters than dimes and five fewer nickels than dimes. How many dimes does Sal have?
A. 13
B. 18
C. 20
D. 21
E. None of these.
Here is the equation I come with but does not lead to the right answer:
25(x + 3) + 5(x - 5) + 10x = 5200
Is this the correct equation?
The problem you're having is that you're using the value of the coins rather than the actual number of coins. Try that instead, because the value of the coins will not affect how many dimes Sal has in this particular question.
Can you give me the correct equation?
I tried 0.25(x + 3) + 0.05(x - 5) + 0.10x = 52 and got the same answer.
So, what's the equation?
No, the equation you have written is not correct for this problem.
To solve this problem, let's break it down step by step and create the correct equation.
Let's assume that Sal has x dimes.
According to the problem, Sal has three more quarters than dimes. So, the number of quarters Sal has would be x + 3.
Also, it is mentioned that Sal has five fewer nickels than dimes. So, the number of nickels Sal has would be x - 5.
The total number of coins Sal has is given as 52. So, the sum of the number of quarters, nickels, and dimes should be 52.
Therefore, the correct equation would be:
x + (x + 3) + (x - 5) = 52
If we solve this equation, we will find the value of x, which represents the number of dimes Sal has.
Simplifying the equation:
3x - 2 = 52
Adding 2 to both sides:
3x = 54
Dividing both sides by 3:
x = 18
So, the correct answer is B. Sal has 18 dimes.