Question
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?
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?
Answers
PsyDAG
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.
Anonymous
idk fam
Anonymous
9
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9
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0
0
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9
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0
0
Anonymous
what is ittttt I have to do my tenmarksssss
Anonymous
I too have to do my tenmarks
Ziyada
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
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