My aunt called me and asked me this because she was trying to help my cousin with his homework. She came up with an answer but my boyfriend has realized that the answer she came up with is wrong and we can't figure it out. Here's the problem:
You have 16 coins that equal $2.00. How many quarters and how many nickels do you have?
We know the answer is 6 quarters and 10 nickels, but what is the equation that is used to solve the problem?
2006-09-20 16:15:36 · 5 answers · asked by Honey 2 in Science & Mathematics ➔ Mathematics
0.25q + 0.05n = 2.00
q + n = 16
Solve the system of equations.
n = 16 - q
plug (16-q) in for 'n' in the first equation.
0.25q + (16-q)0.05 = 2.00
0.25q + 0.8 - 0.05q = 2.00
0.2q + 0.8 = 2.00
0.2q = 1.20
q = 6
n + q = 16
n + 6 = 16
n = 10
2006-09-20 16:19:54 · answer #1 · answered by Will 6 · 4⤊ 0⤋
You need two equations to solve this system of equations. There are two variables and one equation is needed for each variable. First you know that you need a total of 16 coins, so we will make a=quaters and b=nickles. So the first equation is:
a + b = 16
Second you need an equation that show the amount of money. So the second equation is:
.25a + .05b = 2.00 or you could write it like this if you are like me and perfer whole numbers
25a + 5b = 200
So now that you have the equations I'll let you solve it. Good luck.
2006-09-20 16:26:25 · answer #2 · answered by Joshua G 2 · 0⤊ 0⤋
25q + 5n = 200
q+n=16
q = 16-n (so replace the q in the first line with 16-n)
25(16-n) + 5n = 200
400-25n + 5n = 200
400-200=25n-5n
200=20n
n=10
10 nickels, 6 quarters
2006-09-20 16:24:44 · answer #3 · answered by bearhill13 2 · 0⤊ 0⤋
let q be the number of quarters, n be the number of nickels
25q + 5n = 200
q+n = 16
solve for q & n
2006-09-20 16:25:20 · answer #4 · answered by Anonymous · 0⤊ 0⤋
x = number of quaters
y = number of nickels
x + y = 16
x*.25 + y*.05 = 2
2006-09-20 16:46:19 · answer #5 · answered by tronic_hobbist 2 · 0⤊ 0⤋