Question

Dylan has a bank that sorts coins as they are dropped into it. A panel on the front displays the total number of coins inside as well as the total value of these coins. The panel shows 90 coins with a value of $17.55 inside of the bank.

If Dylan only collects dimes and quarters, write a system of equations in two variables or an equation in one variable that could be used to model this situation.




Using your equation or system of equations, algebraically determine the number of quarters and the number of dimes Dylan has in his bank

Answer 1

We set up a system of equations with D representing dimes and Q representing quarters and solved it to find that Dylan has 33 dimes and 57 quarters in his bank.

Step-by-step explanation:

To model Dylan's situation with his bank of dimes and quarters, we can set up a system of equations. Let D represent the number of dimes and Q represent the number of quarters. Since each dime is worth $0.10 and each quarter is worth $0.25, we can express the total value of the coins in dollars as: 0.10D + 0.25Q = 17.55. The total number of coins is given, so we also have the equation: D + Q = 90.

Now we solve the system of equations:

1. 
   
3. 0.10D + 0.25Q = 17.55
4. 
   
6. D + Q = 90

Multiplying the second equation by 0.10 gives us:

1. 
   
3. 0.10D + 0.10Q = 9

Subtracting this equation from the first equation:

1. 
   
3. 0.15Q = 17.55 - 9
4. 
   
6. 0.15Q = 8.55
7. 
   
9. Q = 8.55 / 0.15
10. 
    
12. Q = 57

With the value of Q known, we substitute back into the second equation:

1. 
   
3. D + 57 = 90
4. 
   
6. D = 90 - 57
7. 
   
9. D = 33

Therefore, Dylan has 33 dimes and 57 quarters in his bank.

Answer 2

1). System of equations- D + Q = 90 and D + 2.5Q = 175.50

2). There are 33 dimes and 57 quarters in the bank.

Step-by-step explanation:

Dylan has a bank that sorts coins as they are dropped in it.

A panel shows the total number of coins inside as well as the total value of these coins.

Let the number of dimes in the bank = D

and the number of quarters in the bank = Q

If the panel shows total number of coins = 90

Then the equation will be

D + Q = 90 -------(1)

And the panel displays the amount of the coins = $17.55

Then equation will be

0.10D + 0.25Q = 17.55 [1 Dime = $0.10 and 1 quarter = $0.25]

D + 2.5Q = 175.50 ------------(2)

Now we subtract equation (1) form equation (2)

D + 2.5Q - (D + Q) = 175.50 - 90

D + 2.5Q - D - Q = 85.5

1.5Q = 85.5

Q =
`(85.5)/(1.5)`

= 57

By putting Q = 57 in the equation (1)

D + 57 = 90

D = 90 - 57 = 33

Therefore, there are 33 dimes and 57 quarters in the bank.