Alisha has 11 coins in her pocket. She only has quarters and dimes. The coins in her pocket add up to $2. How many quarters does she have? How many dimes?
11=Q+D
10D+25Q=200
solve for Q, and D, I assume you can do that by substitution.
number of quarters --- x
number of dimes ------11-x
25x + 10(11-x) = 200
solve for x, and all will be revealed to you
To solve this problem, we can set up a system of equations.
Let's say Alisha has x quarters and y dimes.
From the problem, we know that:
1. She has 11 coins, so x + y = 11.
2. The total value of the coins is $2, so the equation for the value is (0.25)x + (0.10)y = 2.
Now we can solve this system of equations.
We can multiply the first equation by 0.10 so that when we add it to the second equation, the y terms will cancel out:
0.10(x + y) = 0.10(11) --> 0.10x + 0.10y = 1.10.
Now we can add the two equations:
(0.25)x + (0.10)y = 2
0.10x + 0.10y = 1.10
____________________
0.35x = 3.10
Divide both sides by 0.35:
x = 3.10 / 0.35
x = 8.857
Since we cannot have a fraction of a coin, we can conclude that Alisha has 8 quarters.
Now we can substitute the value of x back into the first equation to find y:
8 + y = 11
y = 11 - 8
y = 3
Therefore, Alisha has 8 quarters and 3 dimes.
To solve this problem, we can set up a system of equations. Let's say A represents the number of quarters and D represents the number of dimes.
1. The first equation represents the total number of coins:
A + D = 11
2. The second equation represents the total value of the coins:
0.25A + 0.1D = 2
To solve this system of equations, we can use substitution or elimination.
Let's solve it using elimination:
1. Multiply the first equation by 0.1 to get rid of decimals:
0.1A + 0.1D = 1.1
2. Subtract the second equation from the modified first equation:
(0.1A + 0.1D) - (0.25A + 0.1D) = 1.1 - 2
Simplifying:
0.1A - 0.25A + 0.1D - 0.1D = -0.9
Combining like terms:
-0.15A = -0.9
Divide both sides by -0.15 to solve for A:
A = -0.9 / -0.15
A = 6
Now, substitute the value of A back into the first equation to find D:
6 + D = 11
D = 11 - 6
D = 5
Therefore, Alisha has 6 quarters and 5 dimes.