Question 1082722: systems of equations: Larry has $4 in nickels and quarters. If there are 36 coins in all, how many nickels and how many quarters does Larry have.
Found 2 solutions by My Virtual Math Guide, ikleyn:
Answer by My Virtual Math Guide(2)   (Show Source):
You can put this solution on YOUR website! First, let's define variables. Let n = number of nickels, and q = number of quarters. If Larry has $4 in nickels and quarters, then our first equation is
0.05n + 0.25q = 4 (since a nickel is 5 cents, and a quarter is 25 cents)
Since there are 36 coins, then n + q = 36
Now, we have to solve the equation simultaneously. We can use the substitution method. We can rewrite the second equation as n = 36 - q, then substitute into the first equation to get:
0.05(36 - q) + 0.25q = 4
Simplify
1.8 - 0.05q + 0.25q = 4
Simplify further:
1.8 + 0.2q = 4
To find q, first subtract 1.8 from both sides of the equation to get:
0.2q = 4 - 1.8 = 2.2
Now, divide both sides by 0.2 to get:
q = 2.2/0.2 = 11
To solve for n, remember n + q = 36
So n + 11 = 36
subtract 11 from both sides of the equation:
n = 36 - 11 = 25
Now that we have the values of n and q, we can check our answers to make sure we are right.
Equation 1: 0.05n + 0.25q = 4
Let's substitute the values of n and q into the equation to see if it makes the equation true.
0.05(25) + 0.25(11) = 1.25 + 2.75 = 4
Our answer is correct.
Answer by ikleyn(53765)  (Show Source):
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