Respuesta :
Answer:
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 = [tex]\frac{85.5}{1.5}[/tex]
= 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.
By solving a system of equations, we will see that Dylan has 33 quarters and 57 dimes.
How to write the system of equations?
First, we should define the variables that we will be using, these are:
- x = number of dimes that Dylan has.
- y = number of quarters that Dylan has.
We know that he has 90 coins, then x + y = 90.
And we know that the total value in coins is $17.55, so we have:
x*$0.10 + y*$0.25 = $17.55
So the system of equations is:
x + y = 90
x*$0.10 + y*$0.25 = $17.55
To solve the system, you should isolate one of the variables in one of the equations and then replace that on the other equation. I will isolate x on the first one:
x = 90 - y
Replacing that on the other equation we get:
(90 - y)*$0.10 + y*$0.25 = $17.55
Now we can solve this for y.
90*$0.10 - y*$0.10 + y*$0.25 = $17.55
$9 + y*$0.15 = $17.55
y*$0.15 = $17.55 - $9 = $8.55
y = $8.55/$0.15 = 57
So Dylan has 57 dimes. The number of quarters will be:
y = 90 - x = 90 - 57 = 33
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/13729904
