Luis received 15 coins from his dad for chores around the house. Some coins were quarters and others were nickels. If he earned $2.35, how many coins were nickels?
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Let n = nickels
Let q = quarters
We know that that there are 15 coins if you add the n number of nickles and q number of quarters together. So...
n + q = 15
Now, you need another equation that involves $2.35. We know that if we multiply n number of nickles by 0.05 and q number of quarters by 0.25, and then add them together, we will get $2.35. Translate that into a form of equation and you get:
0.05n + 0.25q = 2.35
Now to solve for the number of nickles, which is n, you need those two equations I just gave:
n + q = 15
0.015n + 0.25q = 2.35
Next is solve for q using the first equation.
n + q = 15
q = -n + 15
Plug whatever q is (which is -n + 15) in the "q" on the second equation:
0.05n + 0.25q = 2.35
0.05n + 0.25(-n + 15) = 2.35
0.05n - 0.25n + 3.75 = 2.35
-0.2n = -1.4
n = -1.4 / -0.2
n = 7
There were 7 nickles.
Let q = quarters
We know that that there are 15 coins if you add the n number of nickles and q number of quarters together. So...
n + q = 15
Now, you need another equation that involves $2.35. We know that if we multiply n number of nickles by 0.05 and q number of quarters by 0.25, and then add them together, we will get $2.35. Translate that into a form of equation and you get:
0.05n + 0.25q = 2.35
Now to solve for the number of nickles, which is n, you need those two equations I just gave:
n + q = 15
0.015n + 0.25q = 2.35
Next is solve for q using the first equation.
n + q = 15
q = -n + 15
Plug whatever q is (which is -n + 15) in the "q" on the second equation:
0.05n + 0.25q = 2.35
0.05n + 0.25(-n + 15) = 2.35
0.05n - 0.25n + 3.75 = 2.35
-0.2n = -1.4
n = -1.4 / -0.2
n = 7
There were 7 nickles.
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DO YOUR OWN HOMEWORK!
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10, i think