Respuesta :
Answer:
6 quarters and 9 nickels
Step-by-step explanation:
alright so this took me like an hour or two to figure out cause I'm stubborn. but I wanted to give an in depth answer
..
1) first we need to know how to write it.
___=___+___
1.95 is the full value of all of the coins so it goes here. (___)=___+___
1.95=___+___
We will use q for number of quarters and n for number of nickels. the value of a quarter .25 and the value of a nickel is .05. put the value of a quarter here. ___=(___)+___
1.95=.25q+___
we will put the value of the nickel here ___=___+(___)
1.95=.25q+.05n
now that we know how to write it, we can move onto step two.
2) figuring out what variable n is
n=___
Since we know that there are three more nickels than quarters, we can start to solve this equation.
n=q+3
3) change (n) to (q+3). dont forget to use parenthesis!
1.95=.25q+.05(q+3)
4) i forget what its called but multiply .05 throughout your parenthesis. ill show you.
1.95=.25q+.05(q+3)
.05*q= .05q and .05*3=.15
1.95=.25q+.05q+.15
5) add variables together.
1.95=.30q+.15
6) subtract .15 from both sides to get rid of it.
1.95=.30q+.15
-.15 -.15
1.80=.30q
7) divide .30 from both sides to isolate the q and get the answer of quarters
1.80=.30q
/.30 /.30
6=q
8) add three to the number of quarters to get the number of nickels.
6+3=9 nickels
Here we need to create and solve a system of equations to find the number of coins in the piggy bank.
We will see that there are 6 quarters and 9 nickels.
let's define the variables:
x = number of nickels in the piggy bank
y = number of quarters in the piggy bank.
Knowing that the total value of the coins in the piggy bank is $1.95, then we have:
x*$0.05 + y*$0.25 = $1.95
We also know that there are 3 more nickels than quarters, then we also have:
x = y + 3
Then the system of equations is:
x*$0.05 + y*$0.25 = $1.95
x = y + 3
To solve this, we can see that x is isolated in the second equation, so we can replace it in the other equation to get:
(y + 3)*$0.05 + y*$0.25 = $1.95
Now we can solve this for y:
y*$0.05 + 3*$0.05 + y*$0.25 = $1.95
y*$0.30 + $0.15 = $1.95
y*$0.30 = $1.95 - $0.15 = $1.80
y = ($1.80)/($0.30) = 6
So we have 6 quarters.
Then the number of nickels is given by:
x = y + 3 = 6 + 3 = 9
x = 9
There are 9 nickels.
If you want to learn more, you can read:
https://brainly.com/question/20067450
