Colleen S. answered • 01/14/22
High School Algebra Teacher/Tutor
Hi Noah! The question is asking how many are nickels and how many are quarters. We can define our variables to be n = number of nickels and q = number of quarters. The problem tells us that there are 144 coins altogether. We can write the equation n + q = 144. Since each nickel is worth .05, we know that n nickels would be worth .05n. Since each quarter is worth .25, we know that q quarters would be worth .25q. We are also told that he has a total of $20, so we can write the equation .05n + .25q = 20. You now have a system of equations that you can solve. You could use either elimination or substitution to do this.
Colleen S.
We can solve by substitution. If we solve n + q = 144 for n, we get n = 144 - q. We can then replace 144 - q everywhere we see an n in the equation .05n + .25q = 20. We get .05(144 - q) + .25q = 20. Simplify the left hand side: 7.2 - .05q + .25q = 20. Combine like terms: 7.2 + .20q = 20. Subtract 7.2 from both sides: .20q = 12.8. Finally, divide both sides by .20. We get that q = 64. We can then use the original equation n + q = 144 to figure out how many nickels there are. We get n + 64 = 144. Subtracting 64 from both sides gives us n = 80. So, there are 80 nickels and 64 quarters.01/14/22
Noah Y.
so the answer is N= 4-5q01/14/22