Answer:
To determine the number of dimes in the bag, we can set up a system of equations based on the given information. Let's assume that there are x quarters and y dimes in the bag.
From the problem statement, we know that there are 140 coins in total. Therefore, we can write the equation:
x + y = 140 ---(1)
We are also given that there are 10 dimes for every quarter. Since there are 25 cents in a quarter and 10 cents in a dime, we can express this relationship as:
10y = 25x
Dividing both sides of the equation by 5, we get:
2y = 5x ---(2)
Now we have a system of two equations with two variables. We can solve this system to find the values of x and y.
To do so, let's multiply equation (1) by 2:
2x + 2y = 280 ---(3)
Now we can subtract equation (2) from equation (3):
(2x + 2y) - (2y) = 280 - (5x)
2x = 280 - 5x
7x = 280
x = 40
Substituting the value of x back into equation (1), we can find y:
40 + y = 140
y = 100
Therefore, there are 100 dimes in the bag.
Explanation: