Sam has 18 coins in his pocket that are either quarters or nickels. The total value of these coins is $3.90.
Let q represent the number of quarters and n represent the number of nickels. The following system of equations represents this situation:
q+n=18
0.25q+0.05n=3.90
How many quarters and nickels does Sam have?
Lets first start with what is stated above~
What we know:
Q= Quarters
N= Nickels
Total amount= $3.90
Total coins=18
Q + N= Total coins (18)
0.25Q(Quarter amount) + 0.05N (Nickel amount)= $3.90 (Total amount)
Whenever you do problems like this in a systems of equations unit you MUST ALWAYS isolate only 1 letter, leaving only 1 OTHER letter behind as your new equation
Q + N = 18
-Q -Q
New Equation-
N= 18 - Q
Your next step is simple, plug and chug (don't discriminate, my teacher taught it to me that way, I remember it better in the weirdest way, as you can see)
0.25Q + 0.05(insert the N=18 - Q Equation here)= 3.90
Then simply solve for the equation.
0.25Q + 0.05(18 - Q)=3.90
0.9 - 0.05Q=3.90
Combine like terms
0.25 + 0.9 - 0.05Q=3.90
0.2Q + 0.9= 3.90
-0.9 -0.9
0.2Q/0.2 = 3/0.2
Q = 15
Now for the final step, go back to your N= 18 - Q Equation, and this time, insert your new Q
N= 18 - Q
N= 18 - (15)
N= 3
Your final results
Nickels~3
Quarters~15
This section is for the people who need this equation for homework or for another reason.
18 coins
$3.90
Q= Quarter (0.25)
N= Nickel (0.05)
Q + N = 18
-Q -Q
0.25Q + + 0.05 N =3.90
N= 18 - Q
0.25Q + 0.05(18 - Q)= 3.90
0.25Q + 0.9 - 0.05Q= 3.90
0.2Q + 0.9 = 3.90
-0.9 -0.9
0.2Q = 3
_____ _____
0.2 0.2
Q = 15
N= 18 - Q
N= 18 - (15)
N= 3
Substitute 18-q for n in the second equation and solve for q. Insert that value into the first equation to solve for n. Check by putting both values into the second equation.
idk fam
9
i
9
o0
0
0
what is ittttt I have to do my tenmarksssss
I too have to do my tenmarks
To solve this system of equations, we can use the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the first equation for q:
q + n = 18
q = 18 - n
Step 2: Substitute the expression for q in terms of n into the second equation.
0.25q + 0.05n = 3.90
0.25(18 - n) + 0.05n = 3.90
Step 3: Simplify and solve for n.
4.5 - 0.25n + 0.05n = 3.90
4.5 - 0.20n = 3.90
-0.20n = 3.90 - 4.5
-0.20n = -0.60
Divide both sides by -0.20 to solve for n:
n = -0.60 / -0.20
n = 3
Step 4: Substitute the value of n back into the first equation to solve for q.
q + 3 = 18
q = 18 - 3
q = 15
Therefore, Sam has 15 quarters and 3 nickels.